It is absolutely OK to filter and reuse deep-fry oil.
It's not uncommon at some short-order restaurants for them to filter the oil daily and only change it once a week. Of course, it does start to taste a little "off" when you reuse it that many times.
There's also the matter of impurities lowering the smoke point; even when you filter, the result is obviously not "pure" oil; the more you reuse it, the lower the smoke point gets, and eventually it will actually start to smoke at deep-fry temperatures (i.e. become unusable).
For home use, I'd recommend no more than 3 or 4 reuses. Check the oil to see if it needs to be changed sooner than that - if the colour or smell is off, don't use it again. Best to compare it against a sample of the same "fresh" oil; sometimes it's hard to just eyeball it without a frame of reference. If it looks totally clear and smells fresh, you could probably go up to 5 or 6 reuses - but definitely not more than that.
P.S. There will be some people who tell you that you should never reuse oil for general health (not safety) reasons. My response to that tends to be that if you're eating deep-fried food, you're probably not all that concerned about long-term health risks. Rest assured that if you do a lot of eating out, you've eaten plenty of food fried in "leftover" oil.