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1.
This expression came from the H-game (PC)/PS2/DC/anime Kanon. Ayu Tsukimiya's line (and probably the most famous throughout Kanon). This is her expression when she moans, or whines (like eeeehh, but more original).

Darn though. She had a sad story. One of my few favorites besides Nayuki.
Ayu: I'm cooking cookies.
Yuuichi: I bet they'll taste terrible.
Ayu: Uguu! I've learned how to bake from Akiko-san!
Yuuichi: You can't learn how to bake with just watching in a day..

..although I'll eat them if you manage to make them look good.
Ayu: Really?! Then I'll do my best!
by Welp June 14, 2004
 
2.
When a person is constipated.
"Damn...it's coming...UGUUUUUUUU!!!"
by Peachie November 18, 2007