The importance of pKas in organic chemistry can’t be overestimated, in my opinion. Not knowing pKa’s in organic chemistry is like not knowing the value of the hands in poker. In this scheme, alkyl anions are the equivalent of the royal flush – they win the proton from everything underneath them in the table.
Why are pKas so important? Because every nucleophile is potentially a base, and vice versa. If you have a reaction where it looks like you might get SN2 or E2, look closely first – is there any chance of a simple acid-base reaction? For instance, take NaOH plus an alkyl thiol, R–SH. Is it an SN2? Or possibly an E2? Both are incorrect. The reaction that happens is the simplest one – deprotonation of SH, to provide water and the deprotonated thiol.
Also, the pKa table tells you about leaving group ability. Good leaving groups are weak bases!
If you don’t know the relative values of the pKas of the major functional groups, you’ll be flying blind in the course. Expect to hit a tree.
For more complete lists, be sure to check out Evans, Reich, and Stoltz. (check out the resources on Reich’s page by the way – fantastic!) Blessed are the OCD, for they produce the most beautiful and complete web resources.