Paperboy was my vote; though the first thing that came to mind was MARBLE MADNESS. That was actually a cool game though 
My vote goes to Timber!
http://www.klov.com/T/Timber.html
A game in which the player is expected to chop down as many trees as possible with their trusty axe. If my memory is to be trusted (it isn’t) points are awarded for killing birds.
The Player must always be on the look out for bears desperately trying to save the forest.
Bonus round? Log rolling!
Ahh, good times at Chuck 'e Cheese’s
Ooh! I loved that game! And let me add another wacky Genesis game: Mutant League Football.
Basically, it was a regular old football game of the era, only the team was made up of monsters, and frequent bloody and gruesome deaths occured: you could throw a death pass that was basically a turkey begging to be intercepted, but would explode when the other team grabbed it. You could “sack” the QB- leaving him decapitated.
Great game.
BTW- did everyone know what I game I was talking about in my last post?
Smoke:
Smash TV?
Thanks- I couldn’t remember the title. 
The game was actually Dragon’s Lair (featuring Dirk the Daring and Princess Daphne). It spawned a sequel which had the same game play, but was almost seamless. The main animator for it was Don Bluth who has done a few movies that escape me at the moment.
In addition to Dragon’s Lair 1 and 2, he also had a space game called (cleverly enough) Space Ace. There is a fantastic website with a listing of laser games (including live action ones) at http://www.dragons-lair-project.com/games/.
The strangest of these, and the one that stands out was Thayer’s Quest in that you actually played it with a keyboard that was mounted in the cabinet. Before the game started, you were prompted to type in your name and it would pronounce it for you.
The same team that did “Punch Out” later on did an arcade game that was an arm-wrestling simulator, complete with the fake arm you sat down against and everything.
It was pretty weird, because like Punch Out, each of the opponents had their own personality and unique ‘trick’ to beating them. The one I always remember off the top of my head is Bald Bull from Punch-Out making an appearance as a mysterious hooded opponent. (You had to pull off his hood to stun him in order to finish pushing his arm down onto the table.)
Ooh, I remember that arm-wrestling thing! You had to put your elbow on the pad or else it would call you a cheater and you’d lose. Of course, that didn’t stop you from calling over three friends and hauling that arm down in three seconds on every match.
Oh man, I loveed Zombies Ate My Neighbors! All the good memories are coming back. Fighting the chainsaw freaks, chuckyesque dolls, and giat babies (yes, that was really a level) with fire extinguishers and squirt guns and stuff. I’d buy another sega genesis just for this game.
I remember two versions of Tapper one where you served beer and another where you served root beer.
Crazy Climber was pretty strange.
Journey.
'Nuff said.
Honorable Mention: Lucky Wander Boy.
Don Bluth was the guy behind All Dogs go to Heaven, The Secret of NIMH, and An American Tale, among others. He used to be a Disney animator, but got blackballed when he dared to leave the House of Mouse, which is how he ended up making laserdisc video games, the success of which allowed him to found his own animation studio.
Random anecdote: I know a guy who works at Ubi Soft, and who worked on the new version of Dragon’s Lair for home consoles. As part of the job, he met the guy who invented Dragon’s Lair (not Don Bluth). Apparently, the guy is certifiable. He’s convinced that the release of Dragon’s Lair was an event on par with the moon landing and the JFK assassination. His actual words were something to the effect of, “Everyone remembers where they were on three dates: The first moon landing, JFK getting shot, and the first time they played Dragon’s Lair.” He’s obsessed with the fact that Dragon’s Lair is one of three arcade games kept at the Smithsonian (the other two being Pac-Man and Pong, IIRC). It seems nobody has ever had the heart to tell him his great achievement in life was nothing more than a fad, a cultural curiosity no more significant than the Pet Rock. Kinda sad, really. Mostly funny, but still kinda sad.
The greatest game that never existed? I still have to read that book…
quote: Originally posted by Zebra
It’s actually illeagal in some states to have a game with beer in it where kids can play it. The Budweiser version was in bars only, and the root beer one was for arcades. There was even a version with Suntory beer for Japan.
I still say that Crazy Climber was one of the best arcade games ever. There was a Crazy Climber 2 in Japan only which was 10 time wackier than the first one.
Kid Nikki was another favorite of mine. It was a side-scroller like Super Mario Brothers, chock full of that uniquely Japanese wierdness.
How about Parappa the Rapper? I went from “this is stupid” to “I’m keeping it and never returning it to the rental store” in about five minutes.
And thank you r.j.a. for planting that damn Burgertime music back in my head. I’ve spent years trying to get rid of it. (Play the MIDI from the “Sounds” link here if you’d like to join me in my hell).
Police 911 is cool. It uses motion sensors so that your character on-screen dodges bullets in time with your movements. Konami has a boxing game that uses this same technology as well.
As for rhythm games, forget Dance Dance Revolution, Percussion Freaks is where it’s at. 5 drum pads and a bass pedal.
I spent money a happy weekend playing Zombies Ate My Neighbors and listening to too much heavy metal. It probably explains quite a bit.
Pacman is wacky. Think about it. A disembodied yellow head gobbling up magic pills and running away from ghosts in an endless series of mazes.
You haven’t seen wacky until you’re expected to ram your finger up someone’s ass for thrills. I’ve never played it, as it hasn’t been released in the US (I wonder why…).
Caution: link is probably not work-safe, as the tiny 4-bit graphic of 69’ing might offend somebody. That, and it’s part of an article about the “naughtiest games of all time.” Mods, please remove if I’m violating any link regs.