One of the really cool things about this series is that Universal managed to keep most of the characters and items intact while considerably changing the genre for each release. I'm going to stick with the original four Universal coin-ops and ask you to name your favorite and why.
Mr. Do! (1982)
The original. Thought by many to be derivative of Namco's Dig Dug, but the similarities end with dropping stuff on the bad guys. The game has unique starting patterns, a ball weapon, the ability to rack up bonus points via cherry picking, an E-X-T-R-A meter, the center bonus prize, the chance at the "mystery diamond"... WOW.
Mr. Do!'s Castle (1983)
Back in the day, no one saw this coming. The original game didn't seem "big" enough to warrant a sequel let alone such a change in style. It LOOKS like a platformer but it's definitely a maze game. Lots of neat elements carried over from the original plus the change from throwing ball of death to a hammer weapon truly challenged us then and now.
Mr. Do!'s Wild Ride (1984)
If you didn't expect the original-to-Castle sequel/genre surprise, then surely you didn't expect Mr. Do! to go on yet another ride, this time in a game that's still so very unique. Is it an action game? A puzzle game? We don't care. It's FUN!
Do! Run Run (1984)
I've NEVER seen this in an arcade and even questioned it's existence to a fewllow DP'er right up until about 1990 when someone finally produced an arcade flyer (yeah, this was a bit before info was so easily acquired via the internet). Again, many elements from the Mr. Do! legacy are intact in this maze game that might remind you a little of Taito's Qix.