ドンマイ – This is short for “Don’t mind.” The actual meaning is closer to “No worries,” and it’s usually repeated for emphasis. ドンマイドンマイ. One of my favorites to throw around due to its hilarity.
とんでもありません – I believe this literally means “not at all.” You are basically negating whatever has just been said to you, specifically the heaps of thanks/praise just piled upon you for doing whatever wonderful thing you just did. (Confusingly, とんでもない can also be used as an adjective to mean “not unimpressive.” e.g. とんでもない間違いですよ！ “That is a pretty ridiculous mistake (you moron).” Something like that.)
いいえ・いえいえ – Again, you’re dismissing something someone has said. If you happen to be a dude, make sure you say this in a suitably deep voice. I feel like the intonation requires a slight rise in tone, and if you don’t start at a low enough tone, you’ll end up sounding like a lady.
はい・ほい – Sometimes all you have to do is recognize the person’s thanks with a slightly longer than normal は〜い. I’ve noticed that the people in my office kind of soften it by saying ほ〜い, which is possibly for ladies only?
Updated with a comment from facebook – Yoko, a former classmate, sez:
haha, yeah, ドンマイ is pretty funny. i think ‘ほ～い’ is more of a ojiichan-way of saying はい, but girls use it since the trend nowadays is to use more masculine terms (like when a girl says うまい instead of おいしい) either that or ほ～い is somewhat disrespectful so if a guy says it he might get in trouble :P