Can I get a full list of every set LEGO has ever come out with?
Brickset.com is an excellent website with an inventory of sets stretching back as far as 1966. The list is not 100% complete and the site is not an official site of the LEGO groups so it relies on contributions from fans for its updates.
The information below is from the site itself:
What's in the database? The database does not contain everything that LEGO has ever made or that carries a LEGO logo. The completeness of the database is roughly as follows:
1958-1965: No coverage. The era is too complex to cover adequately, and of insufficient interest to justify spending time researching.
1966-1969: Most regular sets, but excluding brick and service packs.
1970-2006: 98% of sets, and also many extended product lines.
2007-date: 99.9% of sets, and most extended product lines sold at shop.LEGO.com.
Although the database contains many non-brick items ('Gear') that are LEGO branded, it does not contain them all: there are too many to keep track of!
The LEGO Collector's guide is very comprehensive and has been made with a lot of collaboration with the LEGO company.
I can't vouch whether it's more complete than brickset (although I'd think so, it's extremely thick), though, and of course you'll have to buy it, but it's a very nice compilation anyway.
1Page linked to is showing 'Product not available' Sep 17, 2014 at 9:53
Although Bricklink positions itself as a marketplace for trading LEGO items it is usually used as a reference catalog for large number of items. Some of which does not exist anywhere else.
Rebrickable is another website having a good catalog, despite having focus on MOCs and alternate models.
It is best to cross-check several sources when searching for particular set or other LEGO item. My personal preference would be to use two sources mentioned here as well as Brickset suggested in another answer.