This might be a little long, so bear with me!
A number of years ago, a young man who was sometimes a visitor to my house, but not a close friend, killed himself. It was a shock, and very sad, but for some reason I got kind of obsessed with it and went into a deep depression, cried all the time, could hardly eat, etc. My mind kept replaying the last time I had seen this chap, and that picture made me feel terrible. He had started to sit down and tell me something - asked me if I had time to talk. I said "Sure," but then he changed his mind and left shortly after. I didn't really feel guilty, as I had offered to listen, and even tried to encourage him to stay, but the memory was just awful, and wouldn't go away.
This went on for a couple of months, when one day I noticed an ad in a local paper for a clairvoyant medium. While I have an open mind about these things, I've never contacted someone like this before or since, but I just went for it. The woman told me when to come to her flat, wouldn't take my name, didn't want to know anything, just gave me an appointment. (This was in the days before people had all the call tracking stuff on their phones, and the young man's parents had kept his suicide out of the papers.)
When I arrived, she started telling me a lot of stuff, like I've seen these people do on television, "I have a lady here, maybe her name is _______ she has a message for you." She went through a bit of this - nothing made sense. I could hardly get a word in edgeways, and figured she was probably nuts, but I listened politely. Finally, she wound down and asked me why I was there. I simply said "Because of Simon." She then said "Does he look like this?..." And described him in rather impressive detail, small scar on face, the shape of a rather unusual haircut, hair colour, age, build, etc. Then she said "Has he passed over?" I said "Yes." She said "He followed you in, and I wasn't sure what was going on. He's feeling sorry for himself and doesn't want to talk to us, but I've told him that it's not okay to attach himself to people like that, and he needs to move on. He's left us now."
At this point we entered a discussion about what this lady believed happens to us when we die. Having just had this experience, I did, and still do, give a lot of credence to her views. Basically she believed that when someone dies they go to another place, a good place, where they are given choices - they can stay in this place - where they can "learn" as she put it - and if they wish they can become guides or "helpers" to the living, or they can choose to be reincarnated - either right away - or they can decide this later. Sometimes, when people die they have trouble accepting it and hang around, but it's not a good thing. There was more detail, but I don't remember it very well.
The next day I woke up feeling like someone who has misplaced something, but can't remember quite what is missing. It was my "depression". It was completely gone. Much later, I found out that Simon had a long history of terrible mental illness. I hadn't picked this up. The person who told me this also thought that perhaps his death might have been more of a result of a flirtation with suicide than a serious attempt. I suppose all this might account for his unrest in some way.
My personal belief is that there is too much anecdotal evidence for "life after life" to discount it. I also believe that it is difficult for most of us to separate the things that may be manufactured by our brains for lots of different reasons, from a truly spiritual experience like information from our past lives, ghosts, contact with deities, etc. However, I don't take this as a reason not to try, I take it as a reason to keep asking questions. I asked myself whether my medium lady could have been a fake, or whether it was possible that she could have coincidentally known about my friend for some pragmatic reason. While it's not impossible to rule it out completely, I decided that any explanation of that sort that I could come up with was even less likely than the alternative - that she had seen my friend's spirit and sent him away to get on with the next stage of his existence.
One question that many of us have is why souls would be reincarnated into all the many forms of misery that our world has to offer, like ill health, poverty, abuse and so on. The answer which makes the most sense to me is along the lines that when the individual chooses to be reincarnated, at that point they are aware that "life" is something of an illusion, and that it is temporary. One life is not the whole story. Perhaps they choose these seemingly terrible circumstances for some higher reason that we cannot fathom (like the evolution of their own soul - some lesson that they believe they will learn through undergoing this extreme difficulty), and we simply cannot see this because we are so caught up in our emotional response to seeing this suffering on our current plane of existence.

You all have such interesting opinions and stories!