I am assuming you are talking brand new, because if you are talking used, you can get practically anything, well not anything but there is a huuuuuuge variety of sports cars out there for $25,000 or less!!
Brand new it would be tough, be here is a short list of "sporty" cars, not necessarily "sports cars" for right around $25,000 or less...
Mazda Miata MX-5 (one of greatest RWD vehicles ever built, what it lacks in straightline performance it more than makes up for in handling, a car magazine i read had an article where the Miata was pulling lap times around a twisty track that were within a couple seconds of the V-10 powered Viper!)
Subaru WRX (the STi is out of your price range brand new, but the WRX is still a great AWD sporty ride)
Honda Civic Si (FWD is a plus if you live where it snows, but a negative if you are concerned fully on performance)
Mini Cooper S (I personally would not drive one, but it does handle extremely well for FWD and can be modified)
Chevrolet Camaro (the base model V-6 should be right around the cut-off point with your budget, even though its no V-8 it still has a good amount of power while getting better gas mileage)
Dodge Challenger SE (great classic muscle car looks, the base model is underpowered, overweight and oversized, but it looks mean and sounds great)
VW GTi (a good alternative to the Civic Si in my opinion, a great mix of luxury, performance, reliability, and economy)
Pontiac Solstice (not a car I would ever recommend but it is defiintely sporty looking and in your price range)
Dodge Charger SE
Mitsubishi Ecipse GT
Subaru Legacy 3.0R (a great AWD sedan with luxury and performance)