I changed the water pump at 130,000 due to overheating. The OEM pump has flimsy plastic fins within so it may be a good idea to change the water pump on these cars every 75,000 to 100,000 miles as a regular maintenance item.
I took the car to Chevy after smelling gasoline to replace the gas tank filler neck solder joint in 1997. The joint leaked considerably and was fixed for free as per a general recall for 1992 Camaro's.
Overheating can be a problem. One solution can be to use a 160 degree thermostat on the engine for the radiator fluid.
Transient electrical problems. Chevy doesn't have good wiring to start with, but this can be made worse by having sloppy third parties install stereo equipment in your car (personal experience). Do it yourself or get a very good installer to do it. Pay the extra money to get it done right or expect problems down the road from bad splices, etc.
No other problems in 6+ years of ownership.
This little V6 is one of the best performance engines I have ever driven, not for 0-60 times though. The acceleration is average at best, but the gas mileage I have gotten in this car is incredible considering the weight and age. With automatic transmission I regularly get 28 MPG on the highway and around 20 (the absolute worst MPG average) in the city with a 150,000+ mile engine.
The car never uses oil and the transmission fluid is still as red as when I changed it at 135,000 miles. The 700R4 transmission shifts appropriately and has near bullet-proof reliability when fluid and filter is changed every 30,000 miles.
Oil is changed at 5,000 mile intervals with Mobil conventional 10W-30 oil.
Take care to apply silicone spray lubricant regularly to the weather stripping in order to prevent it from drying out and creating water leaks (a common problem).
Easy modifications include K&N air filter and cold air induction for modest performance gains.
Comfort and cargo room is bad for this car, in particular the seats. To add to your comfort find front and rear seats from a 4th generation ('93-'02) car, which can be easily found from wrecking yards for $100 total. Install them in your car and enjoy.
Although any 1992 is fairly slow compared to a newer one, a little known secret is that these cars will easily out-handle any newer stock 4th generation. In fact, with the proper tires it handles very close to an Italian exotic! The car exhibits almost zero body roll in a sharp turn. If you like to carve twisty back roads, buy an '88 to '92 with a manual transmission. You can still have fun with an automatic though.
When treated and maintained well, these cars will last a long time. I now use it as my secondary car for driving to work, but it's still fun. I bought it for $5,000 from a wholesaler when in college and have been very pleased in the 6 years I've had it. Great value.