So I was in Riften and this thief attacked me yelling something about crossing him. Any idea what causes that? I mean, I assume it's not a random because he was in the middle of a city and very obviously after me.

Random attacks can happen in cities, too. Usually the Thief is sneaking around until one of the guards notice and attack him, I believe. Maybe it was just a bug?

Did he also yell, "HERE WE GO!"

If I'm understanding correctly these are the thieves that start appearing in Riften after the Thieves Guild mission 'A Chance Arrangement'. They also can be encountered in Riverwood occasionally. UESP: http://www.uesp.net/wiki/Skyrim:Thief_%28Thieves_Guild%29

Hrmm, interesting. I have never had this happen in the city limits.