I had completely forgotten about that movie. I love Gabriel Byrne, and he was perfect in that film, as were the two boys and that old man who played the one armed dishwasher in "Robin's Nest" (or something) years ago.
Another film mentioned earlier that I can't watch without crying is "Truly Madly Deeply".
Billy Elliot gets me every time. I always watch the last five minutes more than once.
Crouching Tiger, Hidden Dragon brings a lump to my throat.
A couple of scenes in Good Will Hunting, One Flew Over the Cuckoo's Nest and Green Mile for sure.
Tears are guaranteed every time I watch the episode of Stargate SG1 called "Forever in a Day" (but that's cos I'm an SG1 addict)