I can recommend the Dungeons And Dragons Adventure System Board Games
- Castle Ravenloft
(best scenarios of the three, most difficult)
- Wrath of Ashardalon
(included campaign option)
- The Legend of Drizzt
(most beginner-friendly and easiest of the three, strongest heroes)
The heroes only have 4 stats each and each skill mostly has a single die roll modifier that is added to a d20. The setup is quick and they play equally well with 2-5 players. During a scenario the heroes become more powerful by finding equipment dropped by slain monsters or by leveling up. However, the heroes usually don't keep their up-leveled status for the next scenario, so you don't have to deal with tons of equipment and stats every time you start playing.
I think they are even a little easier to play than the aforementioned Mice and Mystics, but Mice and Mystics' advantage is the coherent and awesome story connecting the scenarios, whereas the scenarios in the Dungeons & Dragons games are more or less self-contained.