(With an excursion into essential oils, and none into magical properties)
Probably all cultures have discovered the use of scented smoke for pleasure, ritual, purification and healing.
Incense is used in many forms: woods, resins, herbs, as pastes, powders, and even liquids or oils. What most of us think of as incense today is joss-sticks or cones. While the Joss Stick or "Masala" incense has been in existence for a long time and was brought to China by Buddhist monks around 200 ce, cones as we know them were an invention from Japan in the late 1800's. (http://www.jmw.net/history_of_incense.html)
Regional traditions&history
Near East/ Eurasia
Kyphi
Kyphi is a mixture of unknown composition, although some ingredients are known, and various recipes modern recreations can be found.
In "Isis and Osiris", the historian Plutarch comments that Egyptian priests burned incense three times a day: frankincense at dawn, myrrh at mid-day, and kyphi at dusk.
Wikipedia.org
Israel
The Incense Service -
"He shall take a shovelful of burning coals from the altar that is before the Lord, and a double handful of finely ground incense, and he will bring them (into the inner sanctuary) beyond the curtain" (Lev. 16:12).
And some pagan remains -
Jer 44:17 …we will burn incense to the queen of heaven [and pour out libations to her]…
It is said that the temple incense in Israel contained cannabis (which was known in Iran and Assyria as incense ingredient).
Sula Benet, a Polish etymologist demonstrated in the 1930s that the word for cannabis is kaneh-bosm, also rendered in traditional Hebrew as kaneh or kannabus. The root kan in this construction means "reed" or "hemp", while bosm means "aromatic". This word appears five times in the Old Testament; in the books of Exodus, the Song of Songs, Isaiah, Jeremiah, and Ezekiel. It is also said to have been a component of anointing oil:
"Take the following fine spices: 500 shekels of liquid myrrh, half as much of fragrant cinnamon, 250 shekels of qaneh-bosm, 500 shekels of cassia--all according to the sanctuary shekel--and a hind of olive oil. Make these into a sacred anointing oil” (Exodus 30: 22-33).
Hence possibly a healing activity of anointing oil?
The Roman caholic church
has adopted roman customs of using incense for sacred purposes.
Asia
The origin of many of the most popular incense resins and woods.
China
This jar called boshanlu is shaped like a mountain, symbolizing the abode of the Immortals (China).
http://www.artcn.net
Japan
Kodo & Incense games/competitions
Kôdô is a highly stilyzed tradition of enjoying the scent of Aloeswood, in a way similar to tea ceremony.
Incense games were popular with nobility. These are recorded in the Tale of Genji, a Heian period novel.
The Americas
A popular sacrifical incense is Copal.
It is still used in Dia de los muertos celebrations in Mexico.
Costa Rica, Guanacaste-Nicoya region, about 300-1000
Jaguar Effigy Incense Burner
North Carolina museum of Art
this incense burner is supported by a large snarling jaguar, which is replicated in a smaller version atop the lid. Burning coals and incense were placed in the bowl on the back of the large jaguar, and the smoke escaped through small holes in the lid. The alligator and the jaguar are the two most powerful animals of the aquatic and terrestrial realms in Costa Rica. Because they hunt at night and can see in the dark, they gained even greater power in the minds of humans. These animals were traditionally associated with the power of shamans, religious practitioners who were thought to share the animals' supernatural prowess.
Some incenses traditionally used by north american Natives are white sage (that is not the European herb, nor the sagebrush from the Artemisia genus), cedar, and sweetgrass.
Endangered Origins?
When buying incense ingredients, please be aware of their origin.
Sandal wood (santalum album)
The heartwood of the tree contains the oil. It retains the scent for decades.
The oldest trees have the wood most saturated with the precious oil and are being overharvested. People have died for Sandalwood. Efforts are underway to harvest in a managed fashion but rewards are high, so poaching is frequent. Australia is making efforts to culture red sandalwood, which may be a better idea to buy than white.
Attars are perfumes made from Sandalwood oil. Please be prudent with your buying decisions.
Medicinal properties
Sandalwood oil and its basic ingredient alpha-santalol have reported antiviral and even anticancer activity (http://www.ncbi.nlm.nih.gov).
Agarwood, Aloeswood or Eaglewood
Agarwood is the resinous heartwood from Aquilaria trees, native to Southeast Asia.
The trees occasionally become infected with a parasite/fungus and the resin is produced as a natural immune response to a fungal attack.
The trees are also endangered and efforts to produce from managed supplies are ongoing.
In Europe it is referred to as eagle-wood. In Arabic countries, it is known as Oud. In Japan, Jinkoh. Large quantities are exported to Arabic countries and to Japan.
The Aloes of the Old Testament (Num. 24:6; Ps. 45:8; Prov. 7:17; and Cant. 4:14) and of the Hebrew Bible (ahalim in Hebrew) are believed to be agarwood from Aquilaria malaccensis.
http://www.agarwood.in/history-of-agarwood.html
Excursion - A “difficult” oil…
Please avoid buying rosewood oil. The tropical rosewood tree is highly endangered.
Historically important incenses
Frankincense
Frankincense is a resin from the Boswellia genus. The collecting of frankincense requires an incision is made in the trunk of the tree.
Most will recognize frankincense as one of the gifts of the three wise men at the birth of Jesus. However, the frankincense and myrrh were more valuable than the gift of gold.
By 1000 BCE, myrrh and frankincense were traded in Babylon, Assyria, Egypt, Rome, Greece, and China.
The height of the frankincense trade occurred during the second century CE when some 3000 tons of frankincense were shipped each year from south Arabia to Greece, Rome and the Mediterranean. Most Frankincense comes from Somalia. Trials to plant new stands of Boswellia are underway.
http://www.celestialtides.com
Medicinal properties
Frankincense was commonly used for medicinal purposes. Pliny the Elder, (1st century) used frankincense as an antidote to hemlock poisoning. The Iranian physician Avicenna (10th century) thought that it was good for body ailments such as tumors, vomiting, dysentery and fevers. In China B. carteri is used for everything from leprosy, cancer, gonorrhea and carbuncles, and as an astringent. Francincense has reported anticancer and antiinflammatory activity (http://www.ncbi.nlm.nih.gov).
Myrrh
Myrrh is from the Arabic word murr, which means bitter. The myrrh tree can be found in the Middle East, India and Northeast Asia. Myrrh oil is extracted from the trunk, stem and branches by steam distillation. Some of myrrh oil is said to be an an antiseptic, deodorant, stimulant, and a fungicidal agent. (http://mdmd.essortment.com)
Myrrh has been used in healing difficult wounds (http://www.ncbi.nlm.nih.gov).
Ambergris
Probably the most expensive natural product in the world.
It is formed in the intestine of sperm whales, perhaps to coat the sharp beaks of their main food – squid.
The genuine product or chemical substitutes are used in the perfume industry as a fixative scent.
It can be found on beaches as the whales excrete it - a lucky find.
Raw ambergris fetches approximately US$10 per gram (as of 2006). In the United States, importing, buying, or selling ambergris — including ambergris that has washed ashore — used to be illegal.
However, in 2001 this ruling was overturned, and ambergris was deemed not to be a byproduct of the whaling industry, since the whale expels this substance naturally.
There is currently no prohibition in the buying and selling of ambergris in the United States. wikipedia.org
Using & Burning incense
The easiest are store-bought sticks or cones.
However see my reservations further below.
Cheaper type sticks/cones are usually soaked with cheap perfume oils& dyes.
Blending your own mixtures is less practical but more rewarding.
Basic tools: A sturdy bowl, some earth or sand (bird sand is clean and easily obtainable), or small pebbles.
Charcoal disks, large tweezers and/or a spoon.
Keep all incense in air-tight containers.
Grind with mortar&pestle or a cheap electric coffee grinder.
For burning your own powdered incenses, charcoal disks are recommended. These have a central depression to take up ground resin.
Try oriental stores that sell waterpipe tobacco for a source cheaper than new age stores.
These Self-lighting charcoal disks emit a fairly unpleasand smell of salpeter and are therefore best lit on the windowsill or outside.
Their sparks might also, otherwise, burn holes into your precious man-made fiber altarcloth.
Japanese Bamboo Charcoal blocks are not self-lighting and will take a long time held in a candle flame to light.
(shoyeido.com)
I therefore keep some soaked in alcohol (keep storage container well away from the source of flame). They have no smell but do not load as well with ground incense as the disks.
A nifty little stative to burn resins and herbs very gently. Can be made a litle more cheaply from a metal tea strainer.
http://lederkram.de
Recommended or popular commercial types:
Incense sticks
Most base sticks (blanks) use sandalwood dust, leftover from distilling, adhering to a bamboo core.
Judge for yourself if the recycling aspect redeems the sandalwood used.
Charcoal base is preferable.
My favorite type is Fred Soll (http://www.fredsoll.com).
Japanese sticks:
No bamboo core
Subtle in their range of scents
but heavy use of sandal and aloe wood, hence questionable.
Cones
Again sandalwood or charcoal based, you choose.
Paine products from the eastern USA
paineproducts.com
Balsam fir, red cedar and pinon pine cones and short sticks. The red cedar is nice. The balsam fir has a shamanic air to it but does not work well in rooms.
Arabian Incense
Frankincense tears often coated with styrax. Some coated with gold leaf. A classic and a nice start.
Nag Champa
A popular smell that you might recognize from your trips into esoteric shops.
Satya Sai Baba Nag Champa this can be found very often at market stalls etc. – the guru Sai Baba is very popular with many, but also disputed with rumors of personal misconduct.
Perhaps you want to buy another brand of Nag Champa.
Greek Orthodox incense
Small pastille of mixture “boils” on top of coal – a pleasant mixture of base resin and oils… Rose is lovely. A good product is from Mount Athos.
Sweetgrass braids and sage smudge bundles
Especially the sweetgrass can be expensive. You may want to experiment with your own smudge bundles made from homegrown herbs.
Some pure substances you might like to try -
Resins
Frankincense – see above. Dissolves slowly in alcohol.
Benzoin : A vanilla-like smell – lovely if used sparingly. Purifies the air. Well soluble in Alcohol.
Papier d’armenie is a paper impregnated with benzoin and salpeter that has been used for purifying for about a century.
Mastix : Edible, namesake of the verb masticate – chew – an ancient chewing gum. Used in Roman mulsum (spiced, honeyed wine) and modern greek resinated wines (Retsina).
Styrax : is usually sold as charcoal or wood chips soaked with the essential oil . Keep well locked up in an airtight container, or it may overpower your storage drawer.
Gum Arabic: A carrier for other mixtures (herbs!), almost odorless, water-soluble.
Pine resin – collect your own… thank the trees.
You can find it as hardened tears or softer resin that hardens within a few months.
Balms
a few incense ingredients remain liquid, such as Peru or Tolu balm, a bit messy to handle but also a lovely smell.
Tolu balm hardens with time.
Peru balm has great wound-healing properties.
Woods
Sandalwood - see above
Agarwood – see above
Ocote – a resinous wood from South america
Pine woods – all kinds are good. Cedar for example.
Herbs and spices–
use sparingly and together with a resin to avoid a burnt smell.
Rose leaves
Cinnamon
Juniper – berries or leaves
Rosemary
Cardamom
Pepper
Eisteddfod
“Better do a kindness near home than go far to burn incense”
Chinese Proverb
http://www.japanese-incense.com
The princess had sent perfumes kneaded into rather large balls in two jars, indigo and white, the former decorated with a pine branch and the latter a branch of plum.
Though the cords and knots were conventional, one immediately detected the hand of a lady of taste.
Inspecting the gifts and finding them admirable, the prince came upon a poem in faint ink which he softly read over to himself.
"Its blossoms fallen, the plum is of no further use.
Let its fragrance sink into the sleeves of another." *
The Tale of Genji - Chapter 32:
A Branch of Plum
*Japanese dress, Kimono, were scented with incense on special stands;the plum blossom is a symbol of the ephemeral.
/|\
. I am so thrilled to finally understand how to use incense this way and be able to joyfully burn it as an offering 
] Your efforts have obviously been much appreciated.
congrats -