I am sorry

I am sorry [that I did that].

I apologize.

Please accept my forgiveness.

I feel sorry.

Please forgive me.

Please don't let what I did offend you.

Forgive me.

I made a mistake.

I regret my actions.

Please accept my apologies for doing that (for accidentally knocking you down).

I am sorry [to hear that].

I feel sorry.

That saddens me.

I sympathize.

I offer my condolences.