I'd consider it safe. I have been in Thailand in 2006 right during the time of the coup, and I have been there again (among other times) this December (08) when the yellow shirts were protesting.

Simply stay away from the protests and main government offices, and you'll be fine. That means you can't/shouldn't go to see the temples in Bangkok or the royal palace, but there are many other places too (for temples e.g. Ayuttaya or Doi Suthep in Chiang Mai). I really don't like Bangkok anyways. Most times I have been to Thailand, I have left Bkk on the same day as I arrived, didn't even stay the night. There's so much beauty and so much to do in this country, that there's no reason to waste time in a polluted hot, loud and crazy city. Just my 2 ct ...

Anyways, pretty much all 'action' is confined to hot spots in BKK, and the rest of the country isn't much affected. Regarding personal safety, I think it's a non-issue if you avoid the right places. Your only worry would be public transport, as railway sleepers are a very convenient and economic way of getting around (in and out of BKK mainly). However, government buses are also cheap, and failing that there is a huge private transport industry aimed at tourists. You may pay 20% more (which is still pennies) and have to put up with fellow travellers that are too cool for school, but it'll get you where you want. The tourism industry there is already buggered enough, that you'll find plenty of good deals. Besides, the vast majority of the population are very friendly and helpful (and as a matter of course, peaceful) so long as you respect the culture and meet them with a smile. Nothing ideological, and everyone knows you've got nothing to do with it.

But maybe it'd be wise to leave yellow or red t-shirts at home