The "I'm using a favorite bot and it doesn't mean anything, I just want to see if I can get more followers." favorite (suggested by Simeon Visser)
The "lightweight thanks" favorite.
The "noticeably not favoriting this, despite the fact I'm clearly favoriting other stuff around it" non-favorite.
The "I hope they notice me and follow me" sub-favorite.
The "just reminding you I exist" sub-favorite.
The "conversation has come to a natural conclusion and I want to acknowledge your last tweet without adding anything more to the conversation" favorite.
The encouraging "do more of this" favorite.
The "thanks for mentioning me" meaning, which I mostly picked up from Marc Andreesen.
A secondary bookmark meaning: "This tweet has a link I don't have the time (or suitable device with which) to click right now."
The bookmark meaning: "This tweet has something I may want to refer to later".
The core "I liked this tweet (maybe it made me laugh or I found it informative) and I want the author to know that".
Incidentally, my favoriting has accelerated in recent months:
2007 3
2008 7
2009 45
2010 16
2011 33
2012 276
2013 636
2014 1972 (as of mid-September!)
(given the script I used, the year refers to year of tweet not year I favorited it)
I use Twitter favorites with a variety of different meanings and I'm sure others do too, so I thought I'd start cataloging some of the meanings I've used and seen others use.