Buddhists (at least traditionally) believe in past and future lives. Many neo-pagans also believe in some kind of afterlife without any attendant belief in God. But the two groups represent rather different positions on this in at least a couple of respects. First, most neo-pagans (from my experience) seem to view a future life as something to look forward to, whereas Buddhists (in theory) view further births as a nightmare from which they want to escape.
Second, although the whole idea of 'me' having another life would seem to be premised on a belief that what 'I' am is independent of the body and enduring (if not eternal), Buddhists hold the view that there is no enduring self even within a single life. This causes quite a lot of confusion when it comes to explaining past and future lives and different traditions try to explain the mechanics differently.
There is a long tradition in Buddhism of using the idea of rebirth to terrify people into being good and committing themselves to practice, but at the more 'thinking' end one does sometimes find acknowledgement that whilst the new being inherits the karmic stream of the former, the new 'I' is quite different and in no meaningful sense the same person (effectively someone else gets your dirty washing). In practice, I've noticed that it is not uncommon to find Buddhists who engage a peculiar sleight of hand here, relishing the sense of meaning and purpose conferred by a belief that their practice is undoing the awful ties of samsara whilst at the same time enjoying the comfort of knowing that there's little risk of enlightenment any time soon - rather like the sentiment expressed in St Augustine's prayer: 'grant me chastity, but not yet.'
