Depends on whether or not it's a game in a franchise I'm familiar with. I burn through Halo games on Legendary because I largely know what to expect and troubleshooting any trying parts is usually just a matter of trial and error with different strategies anyway.

Most games I'll play on the default setting and then beat again on a higher setting. I'll bump down to easy if I've already played the game through enough (like my more recent runs of Mass Effect and Mass Effect 2 just building a file to transfer into ME3).