SLIME has been available from MELPA for a while, but only recently did we iron out some annoying bugs. Notably, upgrading the SLIME package no longer results in confusion about where SWANK is.
So, as of SLIME 2.11, once you have the melpa (or melpa stable) repository set up, installing and updating SLIME from within Emacs is pretty easy:
M-x package-install RET slime RETEnjoy!
Update: Oh, if you want to switch to MELPA, make sure you remove your old SLIME location from Emacs's
load-path, otherwise the old version will take precedence.