Besides engine problems caused by oil (lack thereof) or overheating, the big woulda-shoulda-coulda problem that I'm aware of is timing belts: need to be changed at the recommended intervals or they can break and cause expensive problems. So I'd recommend that you figure out if your car has a timing belt (or a chain, if a chain, this becomes a non-issue), and if so, when it was last changed. If you can't answer the "when last changed" question then you need either to do it or to get it done. If you can, just make sure you're within the recommended interval and you should be fine.
Other than that, keep an eye on fluids (see above re: overheating), make sure you use the appropriate blend of antifreeze/water for where you live (i.e. don't freeze the engine block), and you should be fine. If you drive places or in circumstances where breaking down could be a health hazard for any reason (road conditions, weather, isolation, crime), then it could be worth getting the vehicle looked at, or checking it yourself, to make sure things like belts and hoses appear sound and/or have been replaced at the recommended intervals, but otherwise you're probably fine.