The simple answer is, we can either be reborn (punar-janma) and experience life once again, or be liberated (moksha) from the cycle of rebirth (samsara). However, the answer is a bit more complex if we see it geographically and historically.
Around the world, what happens after death can be divided into two schools. Those who believe you live only once and those who believe you live multiple lives.
Those who believe you live only once have broadly three schools—those who believe death is the end, nothing else after that; those who believe after death you go to the land of the dead and stay in this afterlife forever; and those who believe after death you go to either heaven, where you enjoy the rest of eternity, or to hell, where you suffer for all eternity (or maybe until you have been adequately punished and are ready to join the rest in heaven).
Those who believe in rebirth believe you keep coming back from the land of the dead (pitr-loka) to the land of the living (bhu-loka) until you learn the ultimate lesson after which you no longer feel the need for a body. There are variations on this, where you are punished for various crimes in hell (naraka-loka) before you are ready to be reborn, or where you enjoy heaven (swarga-loka), until it is time for your return to earth once again.
Ancient Egyptians built pyramids because they believed in an eternal afterlife. Ancient Chinese, before Buddhism introduced the idea of rebirth, have always believed in the land of ancestors that one has to go to after death. Even today, there are rituals where you offer paper money to ancestors to spend in the land of the dead, from whence there is no return.
While rebirth and re-death (punar-mrityu) are seen as inevitable, Hindus have also believed in the concept of immortality (amrita). The devas who live in the sky and the asuras who live under the death fight over this nectar, as do birds (garuda) and snakes (naga). We hear that asuras have Sanjivani Vidya, by which they can resurrect the dead. This is used by Jayanta to bring Shukra back to life. We hear in the Mahabharata, the serpents have naga-mani, or serpent jewel, that can bring back the dead to life; this is used to bring Arjuna back to life after he is shot dead by Babruvahana.