LEGO brick competitors?
Mega Bloks: the well-known Canadian brand
Oxford toys - review
Hasbro KRE-O
K'Nex - yes, they do bricks too (not sure about compatibility though)
Cobi
Best-Lock
Character Building from The Character Group, a range of licensed products including Dr Who, Deadly 60, HM Armed Forces and Ben 10 to name a few. 


Disclaimer: some of these retrieved from the lugnet off-topic/clone-brands group; they also mention "Art Asylum’s C3 Brand" but the site doesn't seem to work.