Over the years, we've bought mostly Legos because of their quality and variety and number of kits. We have a few Megablocks from Canada, my son is a big fan of Pirates of the Caribbean and MegaBlocks got the contract to make constuction kits for the franchise. A few years ago we spotted some Kids Connection bricks at Wal-Mart, they were extremely cheap and in a neat storage case, so we snatched them up. I've recently discovered another company, Best-Lock out of England.
Legos are to found everywhere. Kids Connection is a brand owned by Wal-Mart, so they're exclusive, but they look a lot like MegaBlocks, so I bet MegaBlocks makes them for Wal-Mart and several other retailers. Mega-Blocks are found everywhere. Toys'R'Us has Best-Lock on their shelves and on their amazon.com portal.
I'm sure there are a dozen different companies that copy Legos or come into their own, these are just the name brands that I've come into contact with.
I just found out that K'NEX also makes good quality bricks that are compatible with Legos, but we don't have any K'NEX bricks, just the sticks and connectors. (thanks westfw!)