One approach I've seen is to first generate the rooms without any doors or corridors between them. Then you go through a second pass adding doors to each room to connect them all to each other. Larger rooms could be allowed more doors, and you could easily verify how many dead ends you have by looking at rooms with only one connecting door.
I can't find the link right now, but I recall seeing a presentation on Path of Exile's random dungeon generation, where they place a Start room, an end Room and then a room in the very middle of the map. Then they randomly add rooms and doors using a similar technique I mentioned above, but ensuring that there's a path from the start room to the middle room, and then the middle room to the end room. This ensures the overall network of rooms is linear, which is better for guiding the player.
Another interesting technique is described here: http://www.reddit.com/r/gamedev/comments/1dlwc4/procedural_dungeon_generation_algorithm_explained/
That might be more complex than you're after, but it could give you some ideas.