Great question. I really enjoy following entire baseball seasons when my team is contending. Watching pro sports is all about entertainment, and as long as my team is in it, that's entertaining.
I'll never be a Yankee fan and say the season was a failure if we win but don't win it all, especially after making the playoffs. Only one club ever wins the last game of any season, and to be totally unsatisfied if that's not your team is unreasonable and elitist.
But last place seasons suck, and drain the fun out of being a fan. As a Red Sox fan, I wouldn't trade this century because of what I went through last century. However, it wouldn't be so bad to be a Cardinals fan; a winning record every single year since 2000, first or second place 15 times, in the postseason 15 times, won 2 WS, lost 2 WS... (ya, to Boston, but we owed them).