Well, it depends on the load you expect. I have a fairly busy web site, 18,350 hits yesterday, and have tried to minimize database object creations. I was fortunatly given free access to the server my site runs on ( a duel p3 667 ) but this is a very busy server with ~15 FTP connections always going at around 50K/sec. and a second (very busy) web site running on it and I never see performance lag.
I have a couple functions that summarize data which I use static variables for, but usually I get away with just creating a new db object whenever I need one. Doing it this way, I still only create 2 or 6 db objects per hit, depending on the page...generally it is 2.
Remember that mysql is one of the fastest connecting databases out there, so unless your database server is not on the same computer as your httpd and there is a small pipe between them, you should be ok.