Unless your product is something that builds on Twitter's platform, I wouldn't recommend it. It means your users don't have a choice about how they're authenticated to your site, and

A) Failwhale, anyone?

B) Twitter doesn't provide serious options for protecting their users' login credentials. It's the same username/password combo which is easily phished & replayable.

Sadly, I've pretty much given up on the hope that we'll have a healthy ecosystem of OpenID providers, but at least Google's login system does offer some two-factor options.

For me, neither. I've got no interest in linking my identity in one online service to my identity in a totally unrelated one.

I've just signed up for a free trial to Netflix and they seem to be determined to force you to link its account to your Facebook one (you can avoid it by signing out of FB before going on the Netflix site, but even if you do that it then attempts to link the two together in the background next time you go on the Netflix page). But I don't want my FB page filling up with a list of things that I've watched. Partly because I may sometimes want to watch something I don't want to broadcast to the entire world, but mostly because I doubt that most of my friends have the slightest interest in keeping track of my everyday viewing habits.