I have heard the limit is 25.
This is correct - with the addition that it is 25 active campaigns, maximum. So for example, you can have more campaigns that are paused, and waiting to be turned on later. But only 25 active at any one time.
Do be aware that often advertisers don't really need multiple campaigns so much as multiple Ad Groups. Within one campaign you can create 100 Ad Groups, and each one can be about a different topic, go to a different URL, and so forth.
Usually, campaigns are reserved for when you need to make some major distinctions. For example at the campaign level you set a daily budget, where in the world you would like the ads to show, on what kind of partner sites, and when you would like the ads to end.
Assuming you want all your ads to run on the same budget, show to the same parts of the world, and on the same partners etc., then you probably need only a minimal number of campaigns, and lots of Ad Groups.
Every advertiser's situation is different, of course, so I'm just generalizing.
AWA