Here you have the list of The Simpsons episodes where we can see Burns and Smithers there.
There's three categories for every episode according the kind of role they have:

Main Role
Secondary Role
Cameo (one or more)

Season 1
"Homer's Odyssey"
"There's no Disgrace like Home"
"Telltale Head"
"Homer's Night out"

Season 2
"Simpson and Delilah"
"Two Cars in Every Garage and Three Eyes on Every Fish"
"Dancin' Homer"
"Bart vs Thanksgiving"
"Bart Gets Hit by a Car"
"One Fish, Two Fish, Blowfish, Blue Fish"
"Homer vs. Lisa and the 8th Commandment"
"Old Money"
"Brush with Greatness"
"Blood Feud"

Season 3
"Stark Raving Dad"
"When Flanders Failed"
"Homer Defined"
"Treehouse of Horror II"
"Lisa's Pony"
"Burns Verkaufen der Kraftwerk"
"I Married Marge"
"Homer at the Bat"
"Dog of Death"
"Brother, Can You Spare Two Dimes?"

Season 4
"Treehouse of Horror III"
Marge Gets a Job"
"Homer's Triple Bypass"
"Marge vs. the Monorail"
"Last Exit to Springfield"

Season 5
"Homer Goes to College"
"Rosebud"
"Treehouse of Horror IV"
"Marge On the Lam"
"Bart's Inner Child"
"The Last Temptation of Homer"
"$pringfield (Or, How I Learned to Stop Worrying and Love Legalized Gambling)"
"Deep Space Homer"
"Burns' Heir"
"Lady Bouvier's Lover"
"Secrets of a Successful Marriage"

Season 6
"Sideshow Bob Roberts"
"Treehouse of Horror V"
"Homer the Great"
"And Maggie makes Three"
"A Star is Burns"
"Lisa's wedding"
"Two Dozen and One Greyhounds"
"Who shot Mr. Burns part 1"

Season 7
"Who shot Mr. Burns part 2"
"Lisa the Vegetarian"
"King size Homer"
"Mother Simpson"
"The Simpsons 138th Episode Spectacular"
"Team Homer"
"Scenes From the Class Struggle in Springfield"
"Homer the Smithers"
"Bart on the Road"
"22 Short Films About Springfield"
"Raging Abe Simpson and His Grumbling Grandson in "The Curse of the Flying Hellfish"
"Homerpalooza"

Season 8
"You Only Move Twice"
"Burns, Baby Burns"
"Bart After Dark"
"Lisa's Date with Destiny"
"The Springfield Files"
"Mountain of Madness"
Simpsoncalifragilisticexpiala(Annoyed Grunt)cious"
"The Old Man and The Lisa"
"Homer's Enemy"

Season 9
"Bart Star"
"Lisa the Skeptic"
"The Joy of Sect"
"Simpson Tide"
"The Trouble with Trillions"
"King of the Hill"

Season 10
"Bart the Mother"
"Doh-In In the Wind"
"Maximum Homerdrive"
"Mom and Pop Art"
"The Old Man and the C Student"
"Monty Can't Buy Me Love"

Season 11
"Beyond Blunderdome"
"Brother's Little Helper"
"Hello Gutter, Hello Fadder"
"Grift of the Magi"
"The Mansion Family"
"Missionary- Impossible"
"Kill the Alligator and Run"

Season 12
"A Tale of Two Springfields"
"Homer vs. Dignity"
"The Computer Wore Menace Shoes"
"Skinner's Sense of Snow"
"Tennis the Menace"
"New Kids on the Blecch"

Season 13
"Treehouse of Horror XII"
"A Hunka Hunka Burns in Love"
"The Blunder Years"
"She of Little Faith"
"Brawl in the Family"
"Sweets and Sour Marge"
"Weekend at Burnsie's"

Season 14
"Treehouse of Horror XIII"
"The Dad Who Knew too Little"
"Mr. Spritz goes to Washington"
"C.E. D'oh"
"Dude, where's My Ranch"
"Scuse Me while I Miss the Sky"
"The Bart of War"

Season 15
"My Mother the Carjacker"
"The Wandering Juvie"
"The Regina Monologues"
"'Tis The Fiftheenth Season"
"Diatribe of a Mad Housewife"
"Milhouse Doesn't Live Here Anymore"
"Simple Simpson"
"Fraudcast News"

Season 16
"Treehouse of Horror XV"
"Fat Man and Little Boy"
"Homer and Ned's Hail Mary Pass"
"Goo Goo Gai Pan"
"The Seven-Beer Snitch"
"Future-Drama"
"Midnight Rx"

Season 17
" Bonfire of the Manatees"
" Treehouse of Horror XVI"
"The Last of the Red Hat Mamas"
"The Italian Bob"
" Simpson Christmas Stories"
" Bart Has Two Mommies"
"The Seemingly Never-Ending Story"
"Kiss Kiss, Bang Bangalore"

Season 18
"Treehouse of Horror XVII"
"Kill Gil Volumes I & 2"
"Little Big Girl"
"Springfield Up"
"The Boys of Summer"
"Crook and Ladder"

Season 19
"He Loves to Fly and He D'ohs"
"Homer of Seville"
"E Pluribus Wiggum"
"Love, Springfieldian Style"
"Any Given Sundance"
"Mona Leaves-a"
"All About Lisa"

Season 20
"Double, Double, Boy in Trouble"
"The Burns and the Bees"
"Gone Maggie Gone"

Season 21
"The Devil Wears Nada"
"Thursdays with Abie"
"Once Upon a Time in Springfield"
"Million Dollar Maybe"
"Boy Meets Curl"
"The Color Yellow"
"American History X-cellent"
"To Surveil With Love"

Season 22
"moneyBART" :bulletyellow:
"The Fool Monty" :bulletred:
"How Munched Is that Birdie in the Window" :bulletyellow:
"The fight before Christmas" :bulletyellow:
"Midsummer's Nice Dream" :bulletyellow:
"Loveis many a strangledthing" :bulletyellow:
"Flaming Moe" ::bulletred:

Season 23
"The Falcon and the D'ohman" :bulletyellow:
"Treehouse of Horror XXII" :bulletyellow:
"Replaceable You" :bulletyellow:
"The Man in the Blue Flannel Pants"
"Politically Inept, with Homer Simpson" :bulletyellow:
"The D'oh-cial Network" :bulletyellow:
"Holidays of Future Passed" :bulletyellow:
"Moe Goes from Rags to Riches" :bulletyellow:
"At Long Last Leave" :bulletyellow:

In case I forgot some episode, tell me.

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Rules (soon)

Contest: [link]

Episode, Video and Quote of the Month: [link]