The simple way to check your reputation is to offer a trade to the AI:
- trade x gold per turn to an AI for 1 gold.
If they don't accept, then your reputation is ruined.
Reputation is also specific to a particular civ. For example, if you had broken a per-turn deal with Japan, then your rep is ruined with Japan and any nation that is friendly with Japan, but any civ that is at war with Japan will still deal with you as if your rep is intact.