If I buy a car that was in an accident, will the title still be clean?

Talk go the main DMV office in the capitol city of your state.  I've heard of some real screw-ups and false information giving by local DMV branch offices.

An accident repair will only show up on a report if it's done at a legitimate shop. There are also a lot of guys who work at those places, but do work in their home shop after hours. They have an advantage of being able to charge less on labor than a full time repair shop, while still doing the same quality of work. They tend to accept cash only, and don't charge tax, and they make no report to Carfax. I highly recommend asking around at your dealership if you get in a situation of needing an expensive repair that insurance won't cover.

Only If the car was "totaled".   The title will reveal that and would not be considered "clean".

Merely being involved in an accident would not necessarily make the title "unclean" 

A 'clean' title only means the vehicle is legally in the seller's name and has no liens registered against it, nothing more.  You can buy a damaged or even salvaged vehicle with a clean title.

The branding (salvage, rebuilt, etc) only happens when the cost of fixing the damage is more than __% of the vehicle's value.  I left the number blank because the percentage varies by jurisdiction, and you didn't say where you live.  If the repairs cost more than the total value (or % thereof), it's a total loss and branded as salvage.

Any salvaged vehicle can be fixed and re-certified as rebuilt, as long as it passes strict inspection requirements.  A rebuilt vehicle can be driven on public roads just like a vehicle that's never been damaged.  Salvage-branded vehicles are not allowed on public roads in most jurisdictions.

DMV offices don't wait until a vehicle is bought or sold to change the branding.  If the vehicle was branded as salvage or rebuilt, it would say that on the title right away.  Selling a salvaged vehicle without telling the buyer it's salvage is a form of fraud, which is a criminal offence in most jurisdictions.

Sometimes. Not always.

"The title is currently "clean/clear,".  The title is clean.

If vehicle has been adequately repaired and you want to buy it you can go ahead and buy it as long as the title does not say salvage title or rebuilt. You run into a salvage title when an insurance company purchases the vehicle from the person that had the accident and then they sell the vehicle with a salvage title and it appears right on the title salvage title. It's a pain in the butt to get the vehicle inspected and recertified to go back on the road I don't ever purchase a salvage title vehicle unless I intend to just use it as parts

Lots of cars are damaged in accidents and repaired without any changes to the title. The only time a title would reflect "salvaged" or "rebuilt" would be if the car was totaled and the original title was cancelled by the insurance company.

Request a Carfax report.