I was in America in 2001 but broke my lease on the apartment I was staying when I was leaving. I have been invited to a wedding; will I be allowed in? I am taking my wife and kids but am scared I will not be allowed back in because of this or even get arrested. I am from the UK.
So you moved out early 14 years ago and are concerned that you are on the watch list? Highly unlikely.
Unless you made a complete mess of the place requiring a complete rebuild, your previous landlord did little more than not return your deposit and put a "for rent" sign in the window. This stuff happens every week, and it is simply not worth the building owner's time to make a case over it. Rental property is civil, not criminal, so the police aren't getting involved either. After 14 years any statute of limitations will have run out too.
If you moved abruptly for serious criminal reasons (drug manufacture, dead bodies in the storage room etc.) you might be in trouble, but in that case someone would have filed for an international warrant a long time ago.