1 - FREE BOOKS!!! Ok I went with the most obvious first, but it's the best reason! I don't often repeat read books because there's just so many out there to discover. The library lets you do that without paying upwards of £5 per title (and that's just for the paperbacks). I especially like the non fiction section for discovering lots of new ideas and subjects.
2 - They order books especially for you! If you can't find what you're looking for just ask at the desk and chances are the staff can find the book you're looking for. If not you can be placed on a waiting list in case they decide to buy the book in - I did this when I inadvertently read the first book in a trilogy and a few weeks later got an email to say they'd got the second book (just for me, I like to think ;))
3 - They have a magazine and newspaper section with comfy chairs! I don't really buy magazines - I may pick up the odd copy of Total Film but to me it hardly seems worth paying £4ish for an hour or so of entertainment. My library has a really good selection with back issues, although I must admit they're not very good at acquiring the new issues on time... (last year I waited over a month for an issue of Marie Claire with Taylor Swift on the cover, but I did eventually get to read it and therefore saved £3.70!)
4 - They have free internet! Now I haven't used the library computers in years, but I know you used to get two hours free every time you went on them, better than nothing.
5 - They have cheap CD and DVD rental! Must admit I've never used this, but my co-worker assures me you can borrow a CD for 50p a week at his library. I think if I found out more about it I'd use the DVD rentals, since I often have those moments where I just don't want to watch one of mine again, and you have to wait for the postman with online rentals. (I don't have broadband at home so streaming movies isn't an option unfortunately.)
6 - They're open at useful times! Mine opens at 9am five days a week, until 7:30pm three nights a week, plus all day Saturday. Even if you can't just stroll in on a weekday morning like me, it's got times to suit everyone.
7 - It's warm and quiet! Ah those elusive elements, peace to ponder and read as well as an almost too toasty environment in which to do it. Bliss. (Although I've discovered the hard way that nursery schools like to visit for story time surprisingly often...)
8 - They have knowledge of the local area! There are unlimited leaflets on local 'hotspots' at the desk, film club and photography club displays in the foyer and a noticeboard that takes up a huge wall next to the bookcases. (They appear to have a knitting group that I've been too shy to join - yet!)
9 - They have knowledge of EVERYTHING! I didn't read many non fiction or classic books as a kid, or even until a few years ago, so it's been great discovering everything I've been missing. We have a HUGE fiction section here, and through the back in a separate room there's shelves and shelves of non fiction, which has become my favourite spot in the library. I always go here first and work my way clockwise around the room, eyeing all the different sections and spending at least an hour picking up interesting titles, sometimes stopping to read for a while. Since leaving full time education I've found learning way more fun when it's not forced, plus it's been good to discover things without staring at a computer screen.
Do you use your local library? If you have any more points let me know!