Considering that Alexander the Great was known for his good looks (and his male lovers) I have to say I wouldn't mind being the reincarnation of one of them.
That being said, I do believe in the possibility of reincarnation (boy that feels like weasels) but I don't know who I might be a reincarnation of. Probably just some Joe Schmoe. Or a Shane Dane.
It's worth noting that, even assuming reincarnation happens, there are non-trivial odds that you aren't the reincarnation of anyone. Depends on how exactly you think it works, but population growth means that it's likely some souls nowadays had no prior body, or no prior human body at the very least.
There are quite a few more dead people than living people, so you could postulate that we do in fact have enough dead people for each person living today to have had a few past lives. If, for example, reincarnation only started happening after ~7 billion people died (cumulative), and those souls have been used and reused over time, each person alive today would have quite a few past lives (around 15, according to one estimate I found of roughly 108 billion total people ever). Of course, in a few years we'll need to start adding new souls to the mix, because population will continue to grow past those 7 billion.
But there's no particular reason to assume that the fundamental mechanisms of reincarnation chose 7 billion as 'the number of souls to be cycled until they are insufficient, then we start introducing new ones'. It would make more sense for reincarnation to have been happening throughout the existence of humans, and new souls to be added all the time as needed. So when there were only a couple million people on Earth, there were a couple million souls, that then got reused a generation later, and so on. We should then expect a proportionally tiny number of people alive today with very old souls (those souls that have been in the cycle since the beginning of humankind) and a lot of people with souls that are barely a cycle or two old (consider that human population has doubled in the last 40 years or so). And some souls that had no prior human host.
And that is, assuming that a once human soul will be human every time after. If you believe that a human soul can go to a non-human animal after death, then the odds that your soul was human even once before drop tremendously.
This is not intended as a criticism of reincarnation itself. I don't believe in it, but for different reasons. This is simply commentary on the fact that reincarnation being true does not guarantee having past human lives.
