There are perhaps way too many episodes where the marriage of Homer and Marge Simpson is put in jeopardy, and then ultimately saved. This list is for episodes where the stability of their marriage is the episode's central theme. Not episodes such as Bart Gets Hit by a Car, where the subject comes up suddenly at the end.
Note: this list will be updated as I review more episodes.
01) Life on the Fast Lane
Season 01 - Episode 09-009
Marge goes bowling to spite Homer giving her a bowling ball as a birthday present, then becomes closely acquainted with fellow bowler Jacques.
02) The War of the Simpsons
Season 02 - Episode 20-033
Tired of Homer's irresponsible behavior, Marge takes herself and Homer to a marriage retreat. Its at Catfish Lake, and Homer's attempts to fish only complicate matters.
03) Colonel Homer
Season 03 - Episode 20-055
Homer becomes the manager of a former bar waitress whose singing he really enjoys. As she begins falling in love with him, Marge worries that her marriage with Homer is in jeopardy.
04) The Last Temptation of Homer
Season 05 - Episode 09-090
Homer becomes attracted to a new female coworker who has a lot in common with Homer, leaving Homer struggling to remain faithful to his wife.
05) Secrets of a Successful Marriage
Season 05 - Episode 22-103
Homer teaches an adult education class on marriage, but the only way he can keep them interested is by telling them secrets about him and mostly Marge. When Marge finds out, things turn real sour.
06) A Milhouse Divided
Season 08 - Episode 06-159
After the Van Houtens have an ugly divorce, Homer realizes his marriage hasn't been much better, and decides Marge needs a fresh start.
07) Natural Born Kissers
Season 09 - Episode 25-203
Marge and Homer need a new spark in their romance, and get one by getting a thrill via public indecency.
08) Brawl in the Family
Season 13 - Episode 07-276
The family gets help from a social worker to work together, but when Homer's ol' Vegas wife comes to town, it really puts a strain on his marriage to Marge.
09) Three Gays of the Condo
Season 14 - Episode 17-308
Homer 'learns' that Marge began to hate Homer when they were going out, and only married him because she was pregnant with Bart. Angered, Homer leaves and starts living with two gay guys.
10) Brake My Wife, Please
Season 14 - Episode 20-311
When Homer loses his driver's license, Marge starts to lose it somewhat, and after a series of events where Marge 'accidentally' hurts Homer, once again their marriage is in trouble.
11) My Big Fat Geek Wedding
Season 15 - Episode 17-330
Skinner and Krabappel's relationship falls apart just before they were to wed, while Homer and Marge are dealing with yet another marital spat.
12) Mommie Beerest
Season 16 - Episode 07-342
Marge spends time at Moe's after Homer takes out a second mortgage to pay for the bar's repairs. Homer becomes worried that Marge and Moe are partaking in an 'emotional affair', and tries to stop it.
13) Mobile Homer
Season 16 - Episode 13-348
Homer is un-insurable. Marge tries to penny-pinch as a result. Homer gets defiant and spends Marge's savings on a mobile home. Neither are rather happy with one another by this point.
14) Bonfire of the Manatees
Season 17 - Episode 01-357
Homer gets in trouble with the mafia again, and the result this time - forcing Homer to have an adult film take place at his house - angers Marge so much she takes up a new passion in manatee care. Or something like that.
15) Milhouse of Sand and Fog
Season 17 - Episode 03-359
Milhouse's parents get back together but they don't pay attention to Milhouse. Bart tries to split them up again so Milhouse can be showered with love once more, but ends up splitting up his own parents instead.
16) Regarding Margie
Season 17 - Episode 20-376
Homer's relationship with Marge nearly ends after Marge suffers amnesia and has no personal bias to prevent her from seeing Homer as the creep he probably is.
17) That '90s Show
Season 19 - Episode 11-411
Does it count as a marriage episode when a flashback reveals Homer and Marge had relationship problems before they married? In the 90s? ...yes.
18) Dangerous Curves
Season 20 - Episode 05-425
A thing Homer and Marge did five years ago at a lodge almost ruins Homer and Marge's marriage today, at that same lodge while a thing they did 20 years ago at that same lodge may save it. Uh huh.
19) Wedding for Disaster
Season 20 - Episode 15-435
Homer and Marge learn their second wedding from earlier was never official, so they try to plan another big wedding, but Marge turns into a 'Bridezilla', causing Homer a lot of grief.
20) The Devil Wears Nada
Season 21 - Episode 05-446
Marge gets hot and bothered from her own calender photos, but Homer is so worn out from being Carl's assistant he never has the energy to satisfy Marge's craving libido.
21) Moe Letter Blues
Season 21 - Episode 21-462
Moe sends a letter to Homer, Apu and Reverend Lovejoy while they're on a boat telling them he's going to leave town with one of their wives.
22) The Spy Who Learned Me
Season 23 - Episode 20-506
Homer gets help from a concussion-induced spy to help fix his marriage.
23) Love is a Many-Splintered Thing
Season 24 - Episode 12-520
Homer being kicked out of the house for a while takes a back seat to Bart having love troubles, but its still a pretty big theme in the episode.
24) What Animated Women Want
Season 24 - Episode 17-525
Marge is fed up with Homer's lackluster attempts at romance, so Homer tries to fix things by attempting several lackluster attempts at romance.
25) Dangers on a Train
Season 24 - Episode 22-530
As Homer secretly prepares Marge's anniversary present, Marge believes Homer forgot again and inadvertently spends some time with a similarly forlorn married man.
26) Specs and the City
Season 25 - Episode 11-541
Homer learns via spy-capable smart glasses that Marge has been going to a therapist because of how screwy a husband he is.
Season 25 - Episode 17-547
Marge notices Lisa is into a boy who acts a lot like Homer and worries that she might marry him or another guy who acts just like Homer. This viewpoint upsets Homer.
28) I Won't Be Home for Christmas
Season 26 - Episode 09-561
Marge gets upset when Homer doesn't come home on Christmas Eve, and kicks him out. When she learns Moe is mostly responsible, she goes out to find and apologize to Homer, whose having a rather odd adventure of his own.
29) Every Man's Dream
Season 27 - Episode 01-575
Homer and Marge break up due in large part to Homer's narcolepsy. Then they find new partners, who are related to one another! What hijinks!
30) To Courier with Love
Season 27 - Episode 20-594
Homer decides to take Marge to Paris to rejuvenate their marriage, but pays for it by being a mob courier.
31) Kamp Krustier
Season 28 - Episode 16-612
Homer and Marge stop having sex after Homer realizes he becomes a productive member of society when he abstains. This is an actual plotline from an episode trying to be a sequel to a Season 4 episode.