The Australian Open, French Open, and Wimbledon do not use a tiebreaker in the fifth set for men and third set for women. They play that final set until someone gets a 2-game lead, no matter how many games are required. But the US Open still uses a tiebreaker in the fifth set for men and third set for women. Why doesn't the US Open forgo the tiebreaker in the final set like the other 3 Grand Slam tournaments?
Ah, the old debate about the 5th set tiebreaker. Some love it, some hate it. If you were to ask the players themselves, I think most would prefer the 5th set to end in a tiebreak so that you don't potentially end up with a 5th set score of something like 20-18 and play an extra 2 or 3 sets worth of games to decide the winner. Personally, I think it's better for fans and people watching matches to not have really prolonged matches that can become boring and lose interest from the fans.
When it really comes down to it though - the real answer involves stuff like television and media scheduling. The US Open has had their "Super Saturday" thing for a long time - where the 2 men's semifinals are played along with the women's final on the second Saturday of the event. In order to make sure the matches conclude in a "timely" manner - the 5th set tiebreak is used to help make sure the men's semifinal matches don't go on for too long and mess up the schedule for the day. Seems like kind of a silly reason but, it is what it is.
If you ask those involved in running the tournament (USTA) you usually get an answer like "it's what makes the US Open unique" or some other PR-scrubbed answer but in actuality it really just boils down to keeping the schedule running smoothly.
Interestingly enough, the US Open introduced the 5th set tiebreak in 1970 - a few years before the other 3 majors switched to playing out the 5th set. Wimbledon's current 5th set rules were changed in 1979, The Australian Open's in 1971, and the French Open in 1973 - to what you see in use today by those events.