Foot-Dragging Divorcee

Couples in fiction who get divorced generally do so in only two ways. Either they hate each other so much as to fight viciously over every piece of property and terms of child custody, or else it's a unilateral decision which the other spouse, still in love with their partner, can't quite bring himself (and it usually is the husband) to conclude. The divorce papers will lie conspicuously on the foot-dragger's desk, still sealed in their manila envelope, until the very end of the deadline for submission. The would-be ex will pester them to get it done, often because they're planning to marry someone else and the wedding date is fast approaching.

When the papers finally do get signed, it's usually after the reluctant spouse has some plot-inspired epiphany about how he needs to get on with his life, set his partner free to live hers, or otherwise accept that it's over. Either that, or the foot-dragger meets a new Love Interest of his own, possibly as a Pair the Spares.

Subversions often end up being a Comedy of Remarriage. Aversions in which a two-timer claims to his or her lover that their spouse is a foot-dragger, but actually has no intention to divorce at all, are also common.

Examples of Foot-Dragging Divorcee include:

Film

In Twister, Bill Harding is only there in tornado-alley at the time because he came there to badger his wife Jo into finally signing the divorce papers. Subverted in that they wind up back together and never do get the papers signed.
Mort Rainey in Secret Window. It gets to the point where even his wife's new boyfriend is nagging him to get it over with.
In Sweet Home Alabama, Melanie returns to her hometown to badger her husband Jake into signing the divorce papers so she can remarry. He does, but at the wedding it's revealed that Melanie herself did not sign them. They get back together.
The John Wayne movie McLintock! has GW McLintock's estranged wife come back into town to demand a divorce, which he will not do because he enjoys making her miserable and knows deep down she doesn't really hate him.
In The Don's Analyst the protagonist falls in love with the estranged wife of one of the Don's sons, who despite no longer loving her or living together and constantly cheating on her, refuses to grant her a divorce because of his macho code. By the end of the movie, the protagonist has won the family around enough with the Power of Therapy that the son finally agrees to the divorce so she will be free to marry the shrink.

Literature

The character who helps the protagonist in Lucky You has long since split up with his wife, and keeps mailing divorce papers, which she won't sign. The protagonist suggests that she (the wife) is refusing because of a lack of control: she wants to be the divorcer, not the divorcee.

Live Action Television

Agent Hotchner on Criminal Minds hesitated for several episodes to sign the papers that divorced him from Haley.
A plot point in Breaking Bad. Skylar threatens to tell the police about Walt's uh... drug problem if he doesn't sign the paperwork, which he refuses to do.
On Friends, Ross and Rachel get married while drunk in Vegas. Ross makes preparations for an annulment, but delays signing the papers because he likes being married to Rachel, and because he's already been divorced twice. When Rachel finds out, she is none too please.
JAG: Mac had an abusive husband who refused to sign the divorce papers. And then he wound up dead and Mac was tried for murder.
On Bones, Angela's husband that she didn't even remember marrying appears and says he has built a house for her. He won't grant her an annulment/divorce so she can marry Hodgins, but by the end of the episode he relents.
In House, Chase drags his feet regarding the paperwork after Cameron divorces him. It came up in "Lockdown".
Subverted on Psych: Carlton Lassiter was in denial about his separation from his wife, and thought they were getting back together when she asked for dinner at their first-date restaurant. She confronted him with divorce papers and he gave a long, foot-dragging speech, but eventually admits he was aware he'd never been good for her. Having gotten that off his chest, he immediately signs the papers.
Rita's first husband, Paul, in Dexter initially refuses to sign the paperwork, despite the fact that she had him sent to prison for domestic abuse. She later gets him to finalize the divorce, threatening to have his visitation rights to his children revoked if he doesn't sign.
On Angel, Doyle's wife shows up with her new fiancé so that she can finalize their divorce. Doyle is naturally mopey, since the only reason she left him was because he found out he was half-demon. Except that it turns out the new guy is also a demon, forcing Doyle to confront his own personal problems.
On Royal Pains, Charlie does this for pretty much the entire first season to his wife Jill, who he left in favor for his job rather than work on their relationship. Despite her wanting him to sign the papers long before he left, he keeps postponing it in an attempt to woo her. However, sometime between seasons 1 and 2, she finally gets him to sign them and he leaves.

Theater

Sleuth begins with Milo Tindle coming to ask the Andrew Wyke to sign the divorce papers for his wife, who is now Tindle's lover. He's reluctant to do that, and you could say the divorce papers become the MacGuffin of the story.