Super Mad Champ (SNES)

According to legend, this game was originally planned to have been a racing spin-off from the Kunio-kun series, though the tie-in was ditched, the game lived on independently. Like Motor Raid and the Road Rash series, it's a motorbike racing game in which the competitors can attack each other as they pass by.

It definitely seems to be influence by the Road rash games, as it features a simple career system, in which the player must spend money to buy and repair bikes and to enter races, while winnig money by placing highly in races.
Although you'll win a prize no matter what place you finish the race in, only the top three prizes are actually more than the cost of entering. Furthermore, only by placing in the top three can the player advance to the next race, rather than repeating it (and paying the entry fee again). Winning isn't the only way to gain money: there are also small bonuses available for every time you hit an opponent, as well as for finishing a lap in a high position. As well as he five race participants, there are also a bunch of guys riding around the tracks in red jumpsuits. Passing or being passed by them doesn't effect your position, but they can be attacked for bonuses, and if they happen to ride by while you're walking around after falling off your bike, they'll dismount and attack you. When this happens, you can beat them up for a hefty bonus (though due to the time taken to

do this, you'll definitely win the race), or you can get on their bike and ride off on it (which is useful if your bike has been destroyed).
The weird thing about this game is something you won't notice until a few races in, once you start buying faster bikes: it's really hard to steer at high speeds! Rather than just taking a nice simple approach to steering, where going faster just means slowing down a little to stay on the road at corners, steering a fast bike in Super Mad Champ is a delicate affair, requiring pressing the accellerate button and the d-pad at just the right times, and holding them just long enough so that you don't skid and fall off your bike in the middle of the road.

Unfortunately, this ruins the game for me. That kind of finicky steering makes the game feel more like the controls are your opponent, rather than the other racers, and it's just not very fun. The first few races are nice, but once you get into the GP1 class races, it's best to just write the game off and start playing something else.

Monster Puroresu (PC Engine)

This game is a bit of a curiosity: it's a turn-based strategy wrestling game! Mechanically, it has more in common with Pokemon than Fire Pro Wrestling. This actually put me off the game when I first discovered it a few years ago: I saw the title and started it, expecting a probably-awful wrestling game along the lines of

Beast Wrestler or King of the Monsters, and greeted by many little boxes of Japanese text, I instantly turned it off.
Years later, I decided to give it another try and I'm glad I did! Although you'll be missing out on little, unimportant things like the plot or the names of moves, most of the stuff actually related to playing the game is expressed through numbers (and in case you're wondering, the plot, according to a website I found long ago is that an evil demon has taken control of the world, and a human scientist has created a group of mutant wrestlers to fight the demon's forces and liberate humanity).
Each wrestler has five stats: HP, ST, MP, SP, and GT. HP and MP are self-explanatory, serving the same purposes they serve in every game. SP isn't so obvious, and its purpose is still somewhat obscure to me. To explain ST and GT first requires explaining how the game works.
The matches are turn-based, and each turn both wrestlers select a move from their repetoire. Moves come in four categories: hold, hit, power and magic. On selecting a move, each wrestler also recieves a

semi-randomly generated number, the wrestler with the highest roll is the attacker and the other defends. Each move also has its own power rating, higher rated moves do more damage, but tend to get lower rolls. The ST stat also determines how likely a wrestler is to get higher rolls, and GT is a temporary stat, which is increased when a wrestler takes damage, and it can be decreased when selecting a move to slightly increase your chance of getting a high number. After moves have been selected, there's a few seconds during which the players tap button I as quickly as possible to affect a blue/red bar determining how much damage the attacker's move does. This repeats until one wrestler's HP is reduced to zero.
While all this is happening, the top half of the screen depicts the action. Although the animation is pretty limited, the sprites are huge and the animation that there is does do a good job. Moves look painful, even when there's very silly cartoonish things going on like heads being pulled off and limbs exploding. The

wrestlers also all have very expressive faces, and amusing reactions to dismemberment and pain, whether their own or their opponents.
Monster Puroresu is a pretty fun game, though it definitely isn't for everyone. If you like any combination of wrestling, monsters and strategy, and you don't mind wading through lots of Japanese text, you should probably give it a try.