Outside of the long term ignore-my-friend/girlfriend approach, is there any way to simply drop a friend/girlfriend? I have one friend that seems to always be busy when I invite her out and it starting to get annoying.
Well…with 38 views and no responses, I’m forced to believe that it can’t be done. 
If you’re trying to drop your partner you can do so by clicking on the love heart over his/her head, then clicking “End Relationship”. Aside from that I don’t believe K2 has the in-built functionality to instantly remove friends and a mod would need to alter the GUI.
You CAN invite friends to events they won’t like. My personal favourite is Chess, as it’s just requires you and them. Make sure you’re in a foul mood (pessimistic, unhappy, etc). A couple of these will end the friendship very quickly 
Chess anyone?
Wayno, should try this in real life
a game of golf or tennis in a thunderstorm is also a good idea 
Soccer in the snow. Works wonders.