Bleach The Kurosaki children are the offspring of a shinigami and a human. Since shinigami are either born ghosts or become ghosts after dying in the living world, and dwell in the Soul Society as a result, that makes the Kurosaki children the offspring of this trope, which occurred when the shinigami parent decided to shack up in the living world for unknown reasons.
Gosunkugi and that one ghost girl are pretty common in Ranma fanfiction.
My Lovely Ghost Kana is about a poor down-on-his-luck guy moving into an apartment haunted by Kana, the ghost of a girl who gruesomely killed herself. When the Unlucky Everydude protagonist is considering suicide, she talks him out of it with her unique perspective on the matter. They end up falling in love, and both of their situations improve dramatically.
Any shipping of Priest Seto and Kisara after the latter's Heroic Sacrifice. (Considering she is some sort of spiritual guardian for him after death, and that the Blue Eyes White Dragon is technically her mind, it's a pairing that's pretty much canon). This includes most forms of Seto Kaiba/ Kisara, unless it's presented as a Reincarnation Romance instead.
Take any of the numerous characters who are technically dead (Yami Bakura, Shadi, Noah, Chris, Ironheart, Mana, Mahad, etc.) and mix in Yu-Gi-Oh!'s notoriously rabid shipping. Stir once.
Maburaho: Being killed doesn't stop Kazuki from having a harem.
Tasogare Otome x Amnesia about the mystery of the ghost of the old school building, who takes a liking to the one guy who can see and touch her.
This is the plot of Ginban Kaleidoscope.
Pretty much the whole point of Steve Guttenberg/Daryl Hannah movie High Spirits.
The film Ghost features a romance between a living woman and her dead boyfriend.
My Boyfriend's Back is about a boy who is killed, and just before he dies the girl he's in love with tells him that she'd go on a date with him if he recovered. So he comes back as a zombie in order to get that date.
Let's not forget Twilight, although not so much anymore after Bella became a vampire.
In Labyrinths of Echo, The Ace of the series once mentioned that for most people the touch of a ghost is very unpleasant, but he must disagree and offhandedly added "if I'll ever want to vary my life with a dalliance, living lasses have no chance". That's from a wizard who once enchanted a deck of cards so that ghosts can handle it without problems and non-enspelled humans can't touch it. Just to see if he can turn into a "ghost" a thing that never lived to begin with.
There was this Canadian book where the protagonist fell in love with a boy during her vacation in Halifax, Nova Scotia, and it wasn't until the end of the book that she realized he was actually a ghost. It's called Gravesavers.
Inverted in the Incarnations Of Immortality novel Bearing an Hourglass Orlene, a beautiful and intelligent woman is technically married to a ghost named Gawain. But, the ghost needs to carry on his family line. So, the ghost tries constantly to set her up with suitors, to produce the heir he needs so he can pass on. However, she has never seen and cannot see Gawain.
This happens with the main character and a ghost named Jesse in The Mediator series.
The hero and the title character of C.J. Cherryh's Rusalka. Two books later, their daughter falls in love with the ghost of the man who murdered her mother.
In Maggie Furey's Aurian books, Aurian's lover dies, but spends the rest of the series jumping in and out of death trying to protect and help her, despite the fact that she's found a new love by then. Death is understandably not very happy about this, and tries to claim all three of them.
Cabal by Clive Barker, the book that the film Nightbreed was based on. The book features a graphic scene between the corpse of the protaganist Boone/Cabal and his girlfriend.
The short story "Tomorrow's Ghost" by R. Chetwynd-Hayes is based around a romance between a Regency-era woman and a modern-day (1980s) man, each of whom believes the other to be a ghost. It turns out that in a time paradox, back in the woman's own day, she killed herself because she could not be with the man from the future and was being forced into a marriage with someone else - thus is a ghost in the present.
Ruddigore: Dame Hanna and Roderick end up together, although Roderick is (arguably) a ghost.
Happens with Mia/Godot (and to a lesser extent other dead/alive pairings) in Ace Attorney. The justification is that spirit mediums like Maya and Pearl can channel the souls of the dead, to the point of taking on their physical forms. And then just about anything could happen.
An odd one appears in the internet Flash GameGuardian Rock in which the titular rock is said to hook up with a hot spirit rock chick and they live together with numerous flower filled baths and occasional quarreling for the rest of their eternal lives.
Aerith still gets shipped with Cloud, despite the fact that Sephiroth killed her.
Reality Warper Yukari and Cute Ghost Girl Yuyuko from Touhou is one of the more common ships in the series. Yuyuko and her bodyguard Youmu also half counts, since Youmu is half-ghost. No, the fandom has no idea how that happened either. This trope being taken to its logical extreme, perhaps?
In Touhou, ghosts are apparently just as corporeal as humans and youkai. Being dead just isn't that important a distinction in Gensokyo.
In the second Dark Parables game, the Frog Prince is immortal and eternally grieving for his lost brides, most particularly his first wife Ivy.
In The Sims 3, ghosts can be interacted with, invited to live with a family, and, yes, can produce ghost children with living Sims.
Pursuing Nageki Fujishiro in Hatoful Boyfriend ends with Nageki recovering from his Ghost Amnesia and departing for the afterlife, with a heartrending apology to the heroine.
In the "Bad Boys Love" route of the full version, the heroine is killed and her brain transplanted into a robot; the route ends with Ryouta choosing to remain with her until she can be restored.
Too Much Information. Ace (who is also The Ace) has a lot of girls gunning for him, but the first one who actually gets with him is noncorporeal. The details of how, exactly, it works, is left mostly to imagination, with only the comment of "It's... messy."
In Gunnerkrigg Court, Mort (a ghost) has a barely-concealed crush on Antimony (still alive). She does not reciprocate.
It's unclear whether he is a dead person or a spirit who was never alive and just happens to appear like a traditional Bedsheet Ghost, though.
Unsounded fans are quick to point out the potential of a romantic relationship between Sette and her undead bodyguard Duane, or at least a father/daughter one.
Homestuck: Almost any pairing with Aradia post mortem is this trope, with the canon example of Aradia/Equius.
Hanna Is Not a Boy's Name: Hanna/Zombie has a large fanbase, possibly due to the fact that the author seems to endorse it herself.