DigDug aka Taizo Hori (DigDug)
This is a classic character from Pac-Man's time. He was supposed to dig into earth and defeat the underground monsters! In Super Smash Karts, he puts his drill to good use by creating gaps. He doesn't appear himself, however... Maybe he's so deep underground you can't see him?
Alex (River City Ransom)
This character is from the Nekketsu series. In River City Ransom, he has to rescue his girlfriend (Wikipedia says Ryan's girlfriend, but that seems unlikely to me since Alex is the first player's character) from a certain villain called "Slick". In Super Smash Karts, Alex does what he does best: Bash people in the face.
R1 (Super Robot Taisen [Wars]: Original Generation)
IT'S A GUNDAM!!! Not really, actually- R1 stands for Real Personal Trooper Type 1 and it is an original robot for the Banpresto game Super Robot Taisen: Original Generation. It is piloted by video game master Ryusei Date. In Super Smash Karts, the R1 will appear and punch anything in its path!
Super Robot Taisen: Original Generation 1 and 2 are the only SRT game to be released out of Japan.
Zaku (Super Robot Taisen/ Super Robot Wars)
Okay, before anyone bashes at me for a including a Zaku which is primarily a cartoon character, hear me out: Super Robot Taisen (or Wars) is a Japan only strategy game that combines different robots from different cartoons. There's been a whole bunch of installments for nearly every video game series meriting at least a slot or two in Super Smash Karts. Anyhow, Zakus are the weakest mobile suits of the Principality of Zeon- They are quite useless, actually. In Super Smash Karts, their task is 1) To find the enemy and 2) Engage in battle with the enemy. Too bad they only just stick around for a while...
Max (Shining Force)
Max is the hero of Shining Force, a strategy RPG that combines Fire Emblem and standard, walk-around-and-explore-stuff RPGs. That's all I know about him and SF but that didn't stop me from including him in Super Smash Karts. In Super Smash Karts, he appears and strikes at whatever is in front of him with his sword.