Well, I've now been using the wiki constantly for just over a month (received my 'Devoted' badge yesterday). Although I joined earlier this year when the co-operation with MusicBrainz was announced, I only did some initial MB<->LyricWiki edits for Madonna's American Life at the time. About a month back, I was adding advanced relationships for Britney's In the Zone album on MusicBrainz, and I decided to add lyric links too and that's when I got hooked :-)
The badge system was certainly a large part of this. I've never seen that on any other wiki, and it certainly makes you want to keep doing stuff to get the next badge. That said, I've put off writing a blog so I'd actually have soemthing to write, rather than just doing it for the badge. My addiction to the site shouldn't come as that much of a surprise; I've been editing MusicBrainz for about three years now and accrued AutoEditor status and some 30,000+ edits. It means I end up reading an article on something and going to check MusicBrainz (and now here) to see whether the information is present; hence my recent edits on The Wanted, turning a page which just listed one song to a series of pages including one for each band member and their new album.
Finding more stuff that needs doing starts me on a new thread of improving that area. It happens with MB and now it's happening with LyricWiki. This is why my edits tend to end up on all sorts of stuff, including music I won't particularly listen to. There does seem to be a lot that needs doing on LyricWiki. I just reorganised Dizzee Rascal's page, fixing duplicates, and I still need to go back and add his most recent album. The same with Basement Jaxx. And today, I found Joe McElderry was missing altogether, so I've added him.
It looks like they'll be plenty to keep me busy. It took me a while to catch onto the use of the star system on the discussion pages (I need to go and review the Britney and Madonna ones again), but that's another motivator now. I'm watching quite a few songs, and need to get round to certifying more. I also like the notion of marking No. 1 singles and I noticed that the set for the UK is clearly short of some; so that's another thing to start on at some point. There's certainly plenty to do!