After all 21 million bitcoins are mined - which will take quite a long time with the block reward reductions, about 60 years if I remember right - miners will still receive transaction fees from solving blocks and advancing the blockchain. Assuming bitcoin value increases on a trajectory that tracks with the increasing difficulty of mining, it should still be worth solving blocks just for the transaction fees. If it's not, presumably miners will find other coins until the difficulty decreases enough for it to be worth mining again without block rewards.