Not to be pedantic but Snapchat is actually from LA and they're very proud of this fact. In the VC context, they did take money from (Silicon Valley) VCs, but their origins and workforce isn't from SV.
Being even more pedantic, SnapChat started in a class in Stanford. They moved to LA because that's where their early users were and where they started to go viral.
(Of course, being equally pedantic about other Silicon Valley companies - Facebook, Reddit, Dropbox, and YCombinator all "started" in Boston, and the critical events in both AirBnB & Twitter's history happened at SXSW in Austin.)
One of the last consumer-facing, blockbuster level startups outside of SV (or California) that comes to mind was Groupon. But I don't consider them to be that great; kind of a fad that took off for a while and is now lingering. When I say blockbuster level startup I mean something that becomes a household name used by mostly consumers. Highly visible companies mostly. I lump LA/SV together because they're in the same state, and there seems to be a lot of inter-funding between the two areas. But I'm also from Chicago so maybe it's just me. Hah.
(Of course, being equally pedantic about other Silicon Valley companies - Facebook, Reddit, Dropbox, and YCombinator all "started" in Boston, and the critical events in both AirBnB & Twitter's history happened at SXSW in Austin.)