Mine was being the last guy on my team alive while playing Horde Mode in Gears of War 2. Everyone was watching me and cheering my name. I felt pretty damned proud when I took out the horde. Of course, we all died during the next wave.
Not playing online, I'd have to say taking on all comers in Street Fighter 2 or two player Tetris Attack (BUY THIS GAME) back in my younger days will always be a fond memory.
*honorable mention goes to Super Mario Galaxy when I was playing co-op with my (at the time) five year old daughter. She was trying so hard to help me out, grabbing star-bits and shooting Goombas. She was so proud of herself, and I was proud, too!!!*