Used cars can be very reliable.
One tip : Don't buy the most complex, luxury-oriented vehicle you can find for the price. Buy a simple and historically reliable model, and have $500 or so put aside for maintenance.
Other notes on buying used :
Check Carfax
Check for maintenance records.
Make *SURE* the timing service has been performed, don't take anyone's word for it.
If possible, have a qualified mechanic give the car a go-over.
Never bring cash to a meeting place, unless it's obviously safe (ie; mid-day in the WalMart parking lot, with a bazillion cameras and roving security)
Evaluate the current owner. It's generally better to buy from middle-aged folk than youngsters who are likely to have driven the car to it's limits.
When possible, find a vehicle with ~100k miles or less. From that point, with excellent maintenance habits, you should be able to wring another 100k good miles out of the thing, and it's much better to have a running car to sell instead of a used-up dead one

AVOID Turbo/SC vehicles as a cheap used option. Performance-oriented models tend to be driven harder by more demanding owners, and the extra service involved often makes the cost of ownership a lot higher on such things as Eclipses/Talons/RX7s/VWs/etc with forced induction.
Manual Transmission. Unless you can't drive a manual, or find a great deal on an auto, the manual-equipped car will get better fuel economy, be easier to maintain, and much less expensive should you need transmission service.
Some general good deals can be found on the following, depending on your needs :
Infiniti G20, a luxury version of the Sentra of all things, that is reliable, easy to work on, has excellent fuel economy, and pretty comfortable. Good feature set.
Nissan Maxima. Great VQ engine (chain, not a belt), and generally high reliability, you see tons and tons of these things out there with 200k+ miles with average maintenance habits. Comfortable.
Mazda Protege. Many Mazdas were less than reliable, but Proteges seem to buck the trend. Kind of basic.
Ford Crown Vic / Mercury Grand Marquis. Lots of old people own these cars, and they have a low-output V8 that seems to last very very long indeed. Big, comfortable, cheap rides. Only serious negative is below-average fuel economy and grandparent-friendly looks.
Honda Civic. Extremely reliable, but these are hard to find cheaply with ~100k miles. Again, sort of a basic vehicle, but well-designed.
Toyota Corolla. See Civic.
Ugly Ducklings. Many vehicles that are actually quite nice/low miles command a poor resale because of limited demand. Great examples are things like station wagons. A vehicle that normally commands ~$5,000 on the used market might be found for $3,000 or less in the station-wagon version.
Light trucks. With the push for everybody jumping on huge SUVs, huge trucks, and trendy crossovers, it's left light trucks out in the cold. Good deals can be had on pretty much any model. Ranger/S10/Colorado/Frontier/B2200/etc/etc.
That should be a good starting point. Post back here with candidates/needs/etc if you wish.