Do the airlines have access to warrants where they can stop people from leaving the country? For example two mistimeaners and a burgulary charge.

What type of warrant? I predict a resounding YES for serious crimes, but for traffic or other minor things I'd say probably no.

Yes US and most Canadian warrants will show up and there is also a "no fly" list.

On most minor issues they would not detain you, ( but could)
If detained they would contact the agency that has the warrant on you to see if they want you held and returned ( since they have to pay to have you returned, not everyone stopped with a warrant will be taken back)

Hello N:

Specifically, I don't believe the airlines, per se, have access to police files. However, flying today is so integrated with Homeland Security, that THEY'LL for sure know about your warrants, and THEY'LL bust you at the airport.

Kind of makes it easy for them, doncha think?

excon

Not as far as I know. If you have a valid passport then you're free to go. Of course, if you come back, you could well face even bigger problems, including having your passport revoked so that you can't ever leave the country again.