I'm travelling within the US and am a British citizen. Can I travel without my passport and just show my UK driver's license instead?
TSA website has a list of acceptable IDs. From this I would read that only a foreign government-issued passport is acceptable for those travelling without the requisite US (or Canadian) forms of ID.
It's worth noting that if you're just driving, then you need either both forms of your UK driver's license if pulled over, OR the paper form + passport.
One point worth noting is that they're REALLY strict on PASSPORT ID for bars and clubs. I've tried and failed several times to use a UK driver's license, and spoken with many travellers with the same problem. Passport really is required.
The US has a number of circumstances where "government issued ID" is demanded and an "out of state" drivers license isn't good enough, escalating immediately to passport. This includes things like checking into a hotel, picking up your badge at a conference and (I am not making this up) buying medication for a head cold. Mark mentioned getting into a bar which is not an issue for me, but the point is that people want to see your ID rather more than I (a Canadian) expect them to, and if you're not local, they want to see a passport. If an internal domestic flight might not mind you using your UK drivers license, that wouldn't mean that once you got into the States you could ship your passport off for visa-getting purposes or whatnot, because chances are you'll need it pretty regularly while you're there.