I've got the 2006 Camry, and it's pretty solid. Not much goes wrong with it.
Do you have the 4 or 6 cylinder engine? My understanding is that the 6 cylinders have a non-interference engine, and hence have a timing belt which should be changed around 90k miles. The 4 cylinders have an interference engine with a timing chain that should last the life of the vehicle. If you have the 6 cylinder model, check the service records to see if the belt was changed.
The transmission fluid on the 2006 model is essentially a "lifetime" fluid (though if I recall the manual correctly, they recommend replacing it at 150,000 miles). Check to make sure it's at the proper level and is still pink/red. If it's not, or shifting is rough, have someone look at the transmission.
The coolant should be pink (it's the Toyota Super Long Life Coolant in the 2006, I'd imagine it's the same in the 2003). According to the service interval site (see below) from Toyota, it should have been changed at 90,000 miles. If not, it shouldn't be that expensive to do now. I'd stick with the Toyota-brand stuff just for peace of mind.
Obviously you should check all the various fluids to ensure they're the proper color and in the proper amount, as well as all the filters. The cabin air filter is behind the glove compartment -- squeeze the sides of the open compartment together and it'll swing downwards. The cabin filter is in a little tray. The engine air filter requires a 10mm socket (or a 10mm hex nut driver) to access.
Check other bits like the CV boots, hoses, spark plugs, and so on. Fix as needed.
Fortunately, the Camry is a rather low-maintenance vehicle. Do the services at the recommended intervals and the thing will last forever.
http://smg.toyotapartsandservice.com/guides.php will have all the factory-recommended service at the various intervals.