If Gladiator were Star Wars, Commodus would be the Emperor. If Gladiator took place in the Potterverse, Commodus would be Voldemort. If Gladiator took place in Westeros, Commodus would be…well, actually, there are too many evil people in Westeros to count.
In short: this dude is evil, malicious, and flat-out bad.
First, he kills his own father. Then, once Maximus starts sniffing around, he orders him executed. After that, he sends his goons to kill his wife and son and torch his house. Once Maximus gets to Rome, he stacks the cards against him—bringing an undefeated gladiator out of retirement and then tossing in a bunch of tigers to make things interesting, for example.
The point is: Commodus is an evil, evil man who kills anybody who gets in his way. (Plus, he's almost perpetually sweaty-looking. Someone get this guy a bandana. Please.)
Commodus' murderous urges have a lot to do with a lust for power. While en route to Germania, he keeps talking and talking about how he knows Marcus Aurelius will name him his successor. In fact, he's convinced himself so thoroughly that he will be named emperor—and he's so bent on becoming emperor—that when Marcus Aurelius tells him otherwise, he kills him.
He wants to be emperor, and he refuses to let anybody else be emperor. And not only that, he wants to do away with the Senate (he talks about it repeatedly). Why? Because the presence of the Senate dilutes his total power.
Now Commodus' thirst for power isn't just about having power for its own sake. It's about being the center of attention.
Commodus is a diva.
Once Maximus shows up in Rome and "wins" the crowd, Commodus loses his mind, and not only because Maximus is still alive and shouldn't be (though that drives him crazy too). It's because Maximus is once again the center of attention, and Commodus merely a sideshow…just like it was when his dad was alive.
In a scene where he's whining and crying like a five year old (he's stomping around like a toddler) Commodus says,
COMMODUS: And now they love Maximus for his mercy.
He can't stand it that the crowd likes Maximus more than they like him, and so he throws a snit fit. He also can't stand it that Lucilla loves Maximus more than she loves him, her brother.
Despite the power he has, Commodus is a fundamentally insecure dude. He's convinced his father didn't really love him, he's always worried about the Roman population not loving him, and, most important, he's secretly worried about the things he's done.
Sure, he doesn't come out and say "Oh deary me, whatever did I do to Maximus' wife?" but he does suggest to Maximus that he and Commodus really aren't that different:
COMMODUS: Are we so different, you and I? You take life when you have to, as I do.
Those are the words of a guy that, despite having absolutely no moral compass, is still insecure about the decisions he's made and desperately wants some company…because company will confer the approval Commodus' insecurity demands. It's the same near the end of the film, where he absurdly suggests that he and Maximus are brothers since they both loved Marcus Aurelius.
A Liar, a Cheater, and a Creep
Now, since Commodus is the ultimate when it comes to insecurity, and since he's determined to have things his way all the time, he has absolutely no qualms about lying and cheating to get his way.
He lies about Marcus Aurelius' death to Maximus, he puts tigers in the arena in an attempt to kill Maximus, he manipulates Lucilla's love for her son in order to uncover the plot to get Maximus out of the city, and he stabs Maximus before their final fight so he can guarantee himself a win (this one backfires).
He's 100% amoral.
Speaking of morals, it becomes clear as the film progresses that Commodus has a really strange sexual fascination with his sister. He asks for kisses on a number of occasions, and we know he's not asking for kisses on the cheek. He really wants to knock boots (or maybe sandals—this is Ancient Rome, after all) with Lucilla, and he often seems to treat Lucius like a son (probably as partly an attempt to win Lucilla's affection).
Yeah: if you thought Commodus needed to tick off any more boxes in the Creep Checklist, he's also got the hots for his sis.
The writers really want us to hate Commodus, and to wish him defeated by Maximus. Lucky for them, we do hate this dude. And lucky for us, he gets his in the end.