Well, for season finales, when I'm pretty sure that the series is going to be back the next year, there's a kind of mixture of impatience and anticipation. Impatience for the re-runs to be over so the next season can begin, and anticipation for the new season to begin, especially if it's like the Season 5 or 6 ending of "Buffy."
For series finales, it pretty much depends on the individual ending. If all of the loose ends are pretty well caught up or there's at least a logical stopping point in the current story, like there was at the end of Season 7, I certainly feel a sense of loss, but I've had too many favorite shows end over the years to get really heart broken over it (I can sense the angry grumbles beginning to rise in volume already.) Besides, there are always DVD's and HULU.Com.
If the series finale is a cliffhanger or there are just too many questions left unanswered, the way Season 5 of "Angel" was, I feel equal parts angry and betrayed. I know that in real life questions are quite often never answered, but I don't watch a show like "Buffy," or "Angel," or "Highlander," or "Dark Angel," or quite a few others I've had to say goodbye to over the years to see realism. I watch to see a story that has a beginning, a middle, and an end. I'm just funny that way. I can accept Crockett, Bowie, and the rest dying in whatever version of "The Alamo" I happen to be watching or reading at the time, because the story is concluded. I watch the show, including sitting through the sponsor's asinine little commercials, and I sometimes even buy their products. I don't think that it's too much to ask in return to be given an actual ending to the story in return.