I do this all the time. I quote your speeches, I quote my speeches, I quote your friends' speeches, I quote my friends' speeches, I quote famous speeches, I quote speeches I saw four times, I misquote random speeches I saw once and can barely remember. Everybody does this. Call us sentimental freaks, plagiarists, or just plain nerds, but that's the truth.
Every year, several people come up with extremely quotable speeches, probably interps. I mean, a platform can be quotable too, but it seems less likely. Frequently-quoted speeches are typically HIs, funny duos, or funny OIs. Humor is just more fun to quote. A non-funny duo, OI, or even a DI can be quoted, but there would probably be only one quotable line in the whole speech which represented some great and powerful moment or turning point. But Humorous Interps often have a lot of lines that we like to say, as I'm sure you've noticed.
Now you may or may not be wondering, as I once wondered myself, what about stuff that is said in debate rounds? Do people quote those too? Well, yes, but that can get a little odd. See, no two debate rounds are exactly alike. So if somebody said something funny in a round, it's quite possible that the only people who will ever hear that line were the ones watching the round. (Unless that line is said a lot). The problem with quoting people in debate rounds is that you can only quote them around people who also saw that very same round. I've done this before. It's tricky, but oh, so fun.
"You're homeschooled." -Me