Wearing tennis shoes until you have a hole in them is not a very good idea. I know a lot of kids do it, in order to use the warranty and get a second pair free. For most people though, it's not worth putting their feet at risk of injury for just a pair of shoes.
First off, the midsole will likely lose most of its cushioning properties long before the outsole wears off, exposing the ankle joint to more shock than necessary.
Then the upper softens, and will provide less support against ankle roll.
As the outsole wears off, it may lose some grip. (This last point depends on the type of outsole though. I had a pair of shoes with a soft rubber outsole that wore quickly, but remained very grippy even after all the grooves were gone.)
Anyway, generally speaking it is a good idea to replace the shoes when they just don't feel that good anymore. I usually wear through a new pair each summer. Start with brand new shoes in May, toss them in the garbage at the end of September.
Wilson BLX ProStaff 90: 368g, 7pHL, SW=352. (Wilson NXT 49lb / Lux AluPower 45lb).