It depends. if is a game that I have played in a long time then I feel like "YEAH, I FINALLY FINISHED THIS, NOW GO TO HELL I DON'T WANT TO SEE YOU AGAIN!!!!" or if is a game that I enjoyed until the last moment(Golden Sun saga for example) I fell anxious like "YEAH, NOW WERE IS THE SECUEL OF THIS?!!?!?!??!!??!" and if is a more short game is a "yeah did it, what's next on the list??". that's why I play many games at the same time, that way I can dump my rage playing more and that's why rhythm and fighter games master race, they never end.
anime is a different thing, you end up attached to the characters and fells sad knowing that is gonna end, that is enhanced if is a bad or sad open end. I let a tear out of my eyes in the last episode of Gunslinger Girl(then I read the manga and learned a lot of other things like that the anime has the episodes shuffled for dramatic effect but that's another story) and I felt pretty bad after finishing Shana 2nd and the third season was nowhere to be seen, I'm feeling the same way now with Chuu2.