This is an interesting question that will vary highly depending on the individual. I think the main considerations to take into account are the variance inherent in the game, your mental state as the day progresses, and simply how much time you'd like to spend on the tables. These considerations are taken under the assumption that you are following proper
bankroll management, but your bankroll could be a fourth factor if you're not managing it well.
The first point regarding variance is important for me because I am trying to build a bankroll (started at $0 in
freerolls, and now it's up to approx. $300). To overcome the variance inherent in the game, you need to put in some pretty decent volume in terms of number of tournaments and
hands played (or get incredibly lucky xD). Therefore, I try to register for as many within my buy-in level that I can still manage to handle. For me, I prefer to play only 4 tables at a time, but I don't mind registering for new tournaments if I bust out early or in the middle of one of the initial four. I personally don't like rebuying because I like to start on an equal footing, but I know that many better players than I rebuy all the time.
The second point concerning mental state typically applies to when you're playing several tournaments for an extended period of time. If you're tilting and it's affecting your play, it's probably not a good idea to continue registering or rebuying. Furthermore, it'd probably be a good idea to take a break, walk around, and clear the head so as not to tilt into any more mistakes in whatever tournament(s) in which you still remain.
For me and the tournaments that I am currently playing (super micros from $.27 to the occasional $4.40 and $6.60 micros/small stakes), the timing works out such that there are sort of two shifts I can choose to take--the morning shift with registrations starting from 0630 through 0830 and the evening shift with registrations starting from 1600 through 1800. My last point (how much I want to play) determines which day(s) and shift(s) I choose to play. Some days I don't play at all and will do some yardwork or auto detailing. Some days I'll play the morning shift and might go really badly, so I'm not in the mood to play in the evening. Or the same is true and it makes me want to play in the evening (not through tilt) to try to get some wins. Or I just want to play all day, then I do!
So, personally, depending on those factors, I play anywhere from 0 - 20 tournaments per day. On an average day, I'd say it's probably around 12.