When Cooper smashes his head into the mirror when he sees BOB's reflection in it and says How's Annie multiple times - I knew then it was all over for Twin Peaks. I'd heard before it aired that the show was being cancelled but that ending really convinced me. BOB WINS !!!!!!!!!!
When it first aired, I cried when Sarah Palmer found out that Laura was dead and when Donna found out. I guess that goes to show how raw and near to the surface a fourteen year old's emotions can be (and how good Lynch is at stirring your emotions)--I mean, at that point (what? 15 minutes into the pilot?) I wasn't even familiar with the characters, but their performances rang so true that I completely cried my eyes out. When Maddy was murdered I lost my everlasting shit and was near catatonic.That stuff still gets me every time, though I no longer shed tears over it ...I wish I still could. I've just seen it so many times at this point that I guess I'm a bit desensitized.
I've almost cried with fear at the end of episode 8. The slow tracking shot through the hospital to Ronette's room where her arms raise and she has the flashes of BOB and the killing. Some of the scariest stuff ever.
In the first season when the Palmers are just overwrought with grief, I usually get a little misty along with them. At the end of FWWM when Coop shows Laura that her angel is back and she is so happy that she is crying, that one gets me as well. And when Coop embraces Truman at the end of Harry's breakdown, saying "we're all like that."
I'm sure there are many more but those are the three that I can think of right now.
"Sleep deprivation is a one-way ticket to temporary psychosis."
Yes, when the end credits rolled on the series and on FWWM knowing there would probably never be any new Twin Peaks again 
"Harry, I'm going to let you in on a little secret. Every day, once a day, give yourself a present. Don't plan it, don't wait for it, just let it happen. Could be a new shirt at the men's store, a catnap in your office chair, or two cups of good, hot, black coffee. Like this." -Dale Cooper