Do Li-ion batteries have the "memory" problem?

This question is about rechargeable batteries. In the old days, I recall that NiCad rechargeable batteries were said to have a “memory” problem; that is, you had to let them drain completely before you recharged them, otherwise they would retain progressively less and less charge when you tried to recharge them and they would soon become worthless.
Then, when NiMH batteries came on the scene, some people said that these are better because they did not have this memory problem. But others said no, that is not correct, these batteries should also be drained completely before recharging.
So, what about the new Li-ion batteries? What is the real story concerning NiMH and Li-ion batteries?