First time: 1995 at the Trocadero in Philadelphia - a tiny venue that holds about 1000 people, maybe less. I was like 14 at the time, and we made a shirt that said "I LOVE THOM" with iron-on letters. We attached a little note to it with a safety pin and threw it up on stage during the show.
My mom took us to the show, and we convinced her to let us stay afterwards to see if we could wait around and meet the band. One by one, they started coming out. Thom was the last one and was wearing a leather jacket. We were all just standing around talking to him, taking photos, getting autographs, etc, and my friend started sort of freaking out. I looked over at her, asked her if she was ok, and all she could get out was, "..he's... wearing... the shirt!"
Thom heard her and then said, "oh you made this? it's brilliant! thank you!"
The letter attached to the shirt had our addresses on it, and about a month later, we each received a letter from Thom in the mail. The envelope was handwritten, and he told us to make fishy faces in the photo.
Second time: we went to see them open for Alanis Morrisette (left before she started!). We brought a little bag of things we wanted to give them with another note in it. When we arrived, we went to our seats, which totally sucked. But we were seeing them at Hershey Stadium, which is an outdoor stadium where you can see the whole backstage area. My friend looked down in that area and swore she saw Thom walking around. So we gathered up all our things and ran down there.
In the time it took us to get there, Thom had walked away, but Ed and Phil were there. We called them over, talked to them for a bit and gave them the little bag with the note. They went and sat down with Jonny and Colin, opened the bag, read the note and passed everything around their little circle. We were obviously kind of freaking out at this point.
After a little while, they all got up and went to the buses. When they finally emerged, it was to go on stage. This was pre-Ok Computer, so we freaked out when they played Paranoid Android and other OK Compy stuff. Just before the 4th song, Thom said, "Oh wait a moment," and pulled out a piece of paper from his back pocket, unfolded it and said, "the next song is dedicated to Dana, Kathi, and Melissa." They played High and Dry, and we freaked the fuck out.
After the show, they came over to us, said hello, signed stuff for us and other people around. Thom was talking to someone else and I said to my friend, "this is the best birthday present ever." (it was my birthday in like 6 days, but this was my gift from my friends.) Thom overheard me, asked whose birthday it was, I told him mine, and he said "happy birthday" and gave me a hug. And right as he was about to hug me, he said, "sorry, I might smell a bit." Oh man! like I cared!