I respond depending on the type of invitation. If it's something informal and my showing up on time doesn't change the other person's plans ("Do you want to join us for lunch on Wednesday? A few of us are going to be at the coffee shop at noon.) then I may give a noncommital answer.

If the get together has to leave at a certain time I'll give a more definite answer as soon as I can.

Formal invitations get formal RSVPs as soon as I can. Sometimes that may take a bit of time depending on my work schedule.

I NEVER do the "fashionably late" thing. I think that's disrespectful to the host. If the invitation says 8pm I'm there at 8:05.