Let me echo VivTech. You dont need to memorize all the algorithms and variants, but you do need to know what is there, so that sometime later when you need a solution, you know where to look. Also you need to dive deeply into some aspect such as sort or lists so that you get a good feel for big O notation and analysis. You may never implement a sort or tree algorithm, but is good to know which one to pick when you need it.

I've never had to use FFT, but sorts, trees, and graph traversal are pretty common.

My introduction to algorithms oh so many moons ago was Sedgewick when it was a single volume in C(?). I found it easy to read and use.