The Arsenal of MLS...
That would be the Columbus Crew, who like the Gunners, hold the record for most league games without a loss. Which is probably the only similarity between the two. I'm only counting regular season games for this, and while the Crew's 19 games undefeated may fall way behind Arsenal's 49, it's still tops in MLS.
Like always, I count games that ended in shootouts as draws. The Galaxy did not lose in their first 12 games in league history, but were surpassed by DC United in 1997, who had a 16 game streak that spanned two seasons. That was the record until the Crew started their run last year.
So who is the Sunderland (was their streak the record?) of MLS? No surprise here, it's the Metrostars. Their winless run also comes out to 19 games, during their hapless 1999 campaign. The Crew originally set that record in 1996 at 13 games.
We could have some new record holders next year, though. San Jose and RSL both carry long streaks into 2006. The Quakes have gone 14 games without a loss, and RSL has gone 12 games without a win. That's 5 and 7 games away respectively. Of course, if the Quakes are playing in Houston, the Cleveland Browns scenario could come into play, where they would start fresh as a "new" team like the Baltimore Ravens, and then it wouldn't count.
Here's a list of the top streaks in MLS league (regular season) play: