The DNR usually says 4" for walking
6-7" for Snowmobile or ATV travel
12+" for small vehicles

Many people will go out with 2.5" of ice but I usually wait for the 4" mark. Just remember that there is no such thing as safe ice. A lake can freeze unevenly and lakes with springs can be very dangerous. If you are new to a lake as far as ice fishing goes I would wait for some other people to go out that may know the lake better or else ask at a bait shop if they are aware of any bad spots.

Don't let anyone fool you, ice fishing is a blast!!! Boat control is no longer an issue!