Did you ever get in that situation where your opponent runs his clock under a minute, and it makes you rush your moves so you don't give him time to think?

yes! omg yes.... so many times.... always lose from blunders that way

If I have significantly more time than my opponent (say, 1 or 2 minutes more when he's in the last 2-3 minutes), I usually try to make the board as complicated as possible, constantly attacking his pieces and trading as few times as possible.

I usually play long games so the time doesn't usually run out. I could however see this happening to me :(

Take your time to think thoroughly and precise about the situation, and try to make it more complex. If you rush your moves you are turning his problem into yours, don't.

I make the first moves very fast... for my 10 sec... usually my opponent looses minutes, because I use uncommon openings... :)... after so much time you already know where you have to go...

And I use this advantage later... usually I think on my opponent move... and you can direct a game especially if you are white. 

Are you talking about live chess? It's all about lag!!