Chief Wiggums
Nelson
The nerd professor guy
My favorite character ever!
And I’ll contribute to the thread, Frank Grimes.
That’d be Professor Frink.
“Professor Frink! Professor Frink!
He makes you laugh! He makes you think!”
Mafia Guy: Johnny Tightlips where’d they hit ya?
Johnny Tightlips: I ain’t sayin’ nothin’.
Mafia Guy: Then what do I tell the doctor?
Johnny Tightlips: Tell him to suck a lemon!
Captain Lance Murdoch
Wiseguy
That’d be Professor John Frink.
Herb Simpson (Homer’s brother)
Radioactive Man
Fallout Boy
Mr. Largo, the music teacher
The Sea Captain
Santa’s Little Helper
That’d be Professor John Nerdlebaum Frink, mhayving!
Not looking at the other posts…
The Simpsons themselves (named in the OP, so, that’d be cheating…)
Abe Simpson
Mona Simpson (does 3 appearances count as ‘fairly regular’?)
Rev. Lovejoy
Mrs Lovejoy
Jessica Lovejoy
Jasper Beardley
Dolph
Jimbo
Kearney
Nelson Muntz
Krusty
Rabbi Krustofski
Sideshow Bob
Sideshow Mel
Cecil Terwilliger (2 appearances? 3? More than one, anyway.)
Duffman
Bumblebee Man
Ned Flanders
Rod Flanders
Todd Flanders
Maud Flanders (… I’ve never noticed Ned’s the only one of the lot who doesn’t rhyme)
Mrs Krabapple
Otto
Principal Skinner
Miss Hoover
Groundskeeper Willie
Lunchlady Doris
Lionel Hutz
Gil
Patty
Selma
Mother Bouvier
Mr Burns
Smithers
Lenny
Carl
Barney
Chief Wiggum
Mrs Wiggum
Ralph Wiggum
Milhouse van Houten
Kirk van Houten
Luann van Houten
Snake
Fat Tony
Johnny Tightlips
(I’d include the rest of Fat Tony’s gang, but I can’t remember their names.)
Apu Nahasanemapettalan
Manjula (see above <_<)
The octuplets (I’m claiming them as a group)
Comic Book Guy
Dr Hibbert
Mrs Hibbert
Cookie Kwan
Lindsay Nagel
The Sea Captain
Disco Stu
Troy McClure
Squeaky Voice Kid
Martin Prince
Uter
Cheri (Sherri? Sherry? The twin of…)
Terri
… And here I run out of steam…including the Simpsons themselves, I manage…64.
WAY better than I thought I’d manage.
I’ll have to confess that “Maud” and “Todd” don’t rhyme. At least around these parts. Around here “Maud” rhymes with “flawed” and “Todd” rhymes with “God”.
Ummm…Maude, flawed, Tod, and God all ryhme…how in the heck do YOU pronounce flawed? 
To contribute:
Jimmy the Squeeler (squeeling makes him feel like a big man!)
Sarcastic Guy (who sounds a lot like Charles Bronson, or at least a lot like a Charles Bronson imitator)
Dissmissive Guy (not sen much anymore, but he doubts his teenage son or daughter is stupid enough to think a wishbone necklace is really cool)
Wealthy Doweger (kill her with a pie)
Rich Texan (owns the world’s fattest race horse)
Herman (he was waiting for Zed so the party could start)
Leopold (he thinks the kids are little FREAKS and they won’t screw with Marge Simpson)
The leprechan
Lefty
Since we already have Johnny Tightlips, I’ll add Frankie The Squealer
Slight hijack, but “flawed” and “God” (as well as Maude and Todd) rhyme around here. What am I missing
I assume you pronounce all of them to rhyme with “awed,”(aw-d) as opposed to “odd.”(ah-d). Some places there is a distinct difference. Others not.
Handsome Pete - “He dances for nickels!”
Hank Scorpio, owner of Globex, awesome boss.
Umm…both of those words ryhme, too. They are all pronounced like “odd”.
How about ‘sawed’ past tense of ‘saw’? Does that sound the exact same as ‘awed’ and ‘odd’?
In other words, does ‘sawed’ and ‘sod’ sound the exact same to you?
ETA: DCnDC, that exchange is my ALL TIME FAVORITE in Simpsons history. I have been a faithful fan since Tracy Ulman, and I have hundreds of favorite quotes, but the lemon one is my favorite.
Okay… You are aware that there are people and places in the world that don’t speak exactly the way you do, right?
Not to mention that they pronounce them in distinctly different ways on the show itself. “Maude” is Maw-d, Rod and Todd are Rah-d and Tah-d.