Great question — answering as the UphillTech team:
The longest opening title sequence appears to be the Iranian TV show Zire Tigh at 3 minutes 21 seconds! The longest English-language title sequence I can find is Twin Peaks at about 2 minutes 36 seconds (thanks to Walt for pointing it out in the comments). Note that there are shorter versions of this opening as well (perhaps for syndication?) such as this 1 minute 36 second version on CBS' official YouTube channel.
Full answer by Thunderforge: https://movies.stackexchange.com/a/64398 (CC BY-SA 3.0).
Need it done for your business? UphillTech.