A CARFAX isn't the end all be all. Accident listed? A bad car fax can be something as simple as a 5mph parking lot crunch, where they replaced a bumper cover. Conversely, not everything gets reported to CARFAX, so check for things like: frame damage, painted areas, irregular tread wear on tires, etc. Services that have been performed don't always show up, so ask if there are any records. And don't just take "it's a clean CARFAX" to mean that it's all copacetic, because if it was wrecked, someone could have just simply not reported it, and gotten it fixed by a third party.
If you're searching for a used car, go with a reputable company. If you have any hesitations at all about the vehicle, ask to take it to a trusted mechanic.