That game would be Downtown Special - Kunio Kun No Jidaigekidayo Zenin Shuugou!! one of my favorite games, TrueHeat's all time favorite since I gave him it. I play it on my Dreamcast, and I beat it today on it! Runs great on the Dreamcast too, fast, full sound, and it's damn fun!
You should play Nekketsu Kakutou Densetsu as it's the coolest fighting game! It's fun because you can throw your enemies into spikes, electric fences, and do all sorts of weird combos, and it has the same type of graphics as River City Ransom (except a ton more animation).
Incase you're wondering:
http://www.psnw.com/~stumpy/main.html
You can get Downtown Special here, as well as a rom patching utility to make it english. (There are 2 english patches)
If you wanna play it on your Dreamcast:
http://nesterdc.emulation64.com/download.html
You need DiscJuggler though!
Okay, enough fun from me.