MathOverflow is currently still on the Stack Exchange 1.0 system. Unlike many of the other old SE 1.0 sites, it had developed a stable community. Since it was working fine (I think Stack Exchange had agreed to keep hosting MO as a 1.0 site for as long as they wanted.), and there were concerns that closer integration with SE would flood it with non-mathematician questions and voters, they held off migrating.
Eventually, a community consensus emerged to migrate to the SE 2.0 network. The main MathOverflow administrator, Anton Geraschenko, came out in favor of migration. However, for some years it was held up in negotiations. The negotiations were largely over how to add it to the main SE network without compromising MO's distinctive research-oriented community, and allowing MO to leave SE in case it doesn't work out.
However, as of 2013-02-06, it appears that migration to the SE 2.0 network is very close. I believe they have already tested a trial migration site. Yesterday, Anton Geraschenko posted on MO's then-meta forum:
Yes. The agreement with Stack Exchange has been settled (and vetted by lawyers). We're in the process of getting some grant money to make a MathOverflow legal entity, and this is holding up the agreement with Stack Exchange (the agreement is between SE and the MO entity). Everything is taking longer than expected, but things really are moving forward behind the scenes--I promise!