I don't have a specific number that I typically carry. It depends a lot on the circumstances.
- If I'm just goofing around I might bring 5-6 different rackets and play with them - some wood, some old graphites, and a matched pair of sticks that I can rely on if things turn more serious.
- For a semi-serious match where I know the player and have an idea what I'll be facing I'll bring 2-3 of the same racket and probably the same string setup.
- If I'm going to a tournament (haven't in a while, but may give it a shot next year) then I'd typically go with 6 rackets in two sets of 3 matched rackets - the rackets may all be the same and the string tension is the difference, or I may pick one racket with a bit more power to it and one with a bit more touch so that I can choose the best setup for the player that I'm matched against. I tend to pick a slightly stiffer frame with slightly tighter strings if I feel like I will be able to constantly attack the net, and slightly softer racket with a slightly lower string tension if I feel like I'm going to need to stay back more. The stiffer racket gives me a nice crisp response on volleys and helps control blocked balls better, the softer racket lets me bend the ball into the court a bit more and helps when looking for pace from the baseline. If I do choose two different rackets then I make sure that they are very similar (ie. Dunlop Max200g and Max300i) so that I can swap back and forth without too much bother.
I typically use older rackets and have a ton of them, so I can set up a matched bag of Max200g and 300i rackets for what most people spend on a pair of current rackets. This gives me more flexibility in matching the sticks I bring to the way I've been playing lately (both in terms of style and quality).
I'm also not a terribly 'competitive' person. I play because I like to spend time on the court hitting a tennis ball. Mixing up my rackets adds to that pleasure. If I go really serious about it again, I'd probably pick up 6 matched sticks and go to tournaments with two or three different string setups.