FWIW, I'm an American, and I don't really mind ties, but I do like to see overtime and extra innings. In general I feel like if a game is close enough that it resulted in a tie, there is added excitement in seeing more of it, not to avoid a tie, but to have more of the game.
What I don't like is forced tie-breakers that have little to do with the actual game. Going to penalty kicks in soccer is the absolute worst. It has nearly nothing to do with actual soccer. There's no running, passing, dribbling, defending, spacing the field, and the keeper can't even come off the line! The only thing it has to with soccer is that involves kicking a ball. It would be like breaking ties in baseball by taking turns swinging a bat at a pinata... But even though it's not related to the game, a lot of people like this anyway, just because it's exciting to have the game on the line. It's the same reason people like to gamble in casinos. Regardless of the game you're playing, you're invested in something and will be thrilled if you win.
The NHL recently decided to have shootouts in regular season games, and a few years before, they added something like a shootout to college football. Each team takes turns getting the ball at the opponents 25 and scoring until someone screws up... It's a little more related to the game than a shootout, but not enough (imo). It's just about red-zone offense and defense, neglecting anything about working for field position. And to make it even more insulting, they add the score to game score instead of having a separate parenthetical score like in other sports with shootouts! Can you imagine if a soccer match scoring 1-1(5-3) was instead called 6-4?
I think the NFL way of breaking american football ties is much better. Just play an extra period sudden death (with a restriction to prevent the game from ending on a field goal by the first team to possess the ball). This makes it essentially like continuing the game with the same rules (a little different since you're more likely to settle for a field goal than go for a touchdown). There are still ties, but rarely, and it's okay. I'm actually watching more football, not a shootout. However, most other Americans I talk to like the college football method better and it blows my mind... I guess it's just the general love of scoring...