Limited Advancement Opportunities: It's pointed out several times that he is permanently stuck in his position as an associate at Crane, Poole & Schmidt due to his complete refusal to play by corporate rules, but he's simply too good and valuable as a trump card to fire him.
The Lost Lenore: His wife passed away just as he was deliberating over getting rid of her. Since then, he drowns his loneliness and grief in a parade of comely paralegals.
The Only One: He's the go-to man when it comes to impossible cases, since his originality may be the thing to save the day. Also, a lot of such cases are so fucked that there's nothing he can do to screw it up even more.
Hidden Depths: He can be surprisingly insightful and emotional when caught in a quiet moment.
Hypocritical Humor: He claims to have never lost a case, and frequently proclaims "Still undefeated!" after a win. However, he has been shown to lose several cases, though he purposefully takes second chair on cases that he thinks might be losses so that he can claim that it was the first chair attorney, not himself, who earned the loss. Despite that, he still claims the victory on cases won with himself as second chair.
The Not-Love Interest: For Alan, to the degree that, when Denny decides he wants Alan to inherit his estate when he dies, they get married to seal the deal.
Showy Invincible Hero: Denny never lost a case and he never does over the course of the show, but his insane behavior in court only makes it more fun.
Actually, he loses several. See "Hypocritical Humor" above.
Straw Character: Denny Crane is a strawman political caricature of a conservative gun nut, although this did allow him to save the day a few times. Keeping guns in your office seems so much less crazy when you just used them to shoot the man about to kill your best friend.
The Bus Came Back: It never really left. He just moved to a position in the firm where he dealt less with the named partners when Carl transferred to Boston to act as Denny's handler. Paul seems to be happy about this when we see him next, and it's implied that he was burnt out from having to put out all the fires Denny started.
Artistic License: When first introduced, Jerry's disorder is not named, and could be Aspergers, due to his inability to make eye contact and discomfort at having to actually speak to anyone. However, as it progresses, it's pretty clear that it cannot be Asperger's. Asperger's patients have a seeming inability to make friends or empathize with others. This hardly describes Jerry, who considers Alan a great friend, and empathizes with Alan, Shirley and Katie, among others.
Extreme Doormat: His actual personality. He developed Clarice, Clavont, and the others as a way of being able to become someone else that didn't have his crippling shyness.
Grew a Spine: Starts off unable to be himself around others, using his invented personas, and refuses to even try to practice law. By the time he leaves the show, he has more than once defended a client in court and has developed the ability to stand up for himself.