I use a standard hobby knife (the ones with the snap off pieces) and follow the "be careful" approach.

Things that seem to help cutting good curves are:
1. Make sure your blade is sharp (curved cuts seem to blunt the edge faster)
2. Turn the piece, rather than your hand, as you work around the curve

Final piece of advice: Keep hydrated (i.e. make sure you have a drink). Really! Being thirsty is a surefire way to mess up a careful cut!

Good point.
I do a rough cut first, slightly out from the edge, to remove the bulk of the waste card. Then, when it comes to the final cut, the remaining waste peels away from the cut in a thin strip - seems to make it easier to guide the knife accurately around the cut.

(Edit: it's 3am here and I've been working on this monster proposal for way to long and haven't actually cut anything for a couple of weeks, except my fingernails, so what do I know. That's it, time I got some sleep and finish this 'wonderful' proposal tomorrow - never know, I might get some weekend after all! - tired and rambling, Zen)
(p.s. wish me luck )

Following on from Greasius' post: You could try decoupage scissors (small, slightly curved blades with longer handles).

If I'm cutting a circle (or part thereof), I sometimes use a compass cutter to score the circle first. That makes it easier to cut with a blade. Generally, though, I use a fresh blade, a lot of patience and quite a few expletives.

Mandy.

Thanks for all the replies. I ended up using a small pair of scissors for the bridge arches, turned out okay.