GP is something that is always present in FIRST, from the whole concept of alliances to picking to having pits and sharing with teams, but a few examples stick out in my head.
In 10,000 Lakes, our intake roller bent a good 3 inches up, so it would spin wildly off center. If we kept it on it could end up cracking our whole chassis basically or leading to other equally catastrophic failures on the robot, but we didn't have the 25 inch shaft needed to replace it, since standard sizes end at 24 inches. Our options would be to make ball collection significantly harder by removing it, or use it, wait for it to fail, and become a glorified kitbot. I don't think anyone outside of the pit crew knew how totally sunk we were.
Some kind folk from Team 93 went and machined a new roller and shaft for us. It ended up weighing a few ounces more, but it was not a problem at all, and they helped us even when they had a match with us. They still ended up winning thanks to a stupid mistake on my part, though.
The best part? I have three more examples of that. In FVC, our team took a completely failed robot and built them a squarebot in 15 minutes, which was a lot of fun. The next year, that team helped my new FTC team rebuild a modified squarebot to go on to beat them, and win the entire event. After that, in Atlanta the FTC team next to me rebuilt my manipulator with me, and I ended up winning a match with that! (Even though the drivetrain failed, repeatedly and catastrophically, every match)
The thing is, when I tell this to non-FIRST people they're shocked that it would happen. When I tell it to FIRST people, it's not "expected" but it's the kind of thing that happens everywhere. And honestly, it's pretty amazing to be part of an organization where helping your opponent potentially beat you in the name of fair, fun, friendly competition is not only applauded, but the norm.