There are three Maison Ikkoku OVAs, although only the middle one contains original material. The first and third are edited compilations of clips from the TV series, but slightly surprisingly they both do something interesting with this and I'd recommend them.
The first one, Through the Passing Seasons, is a summary of the series. Yes, all 96 episodes. Completely mad, right? In fact, no, it isn't. It works much better than you'd expect, telling the essential story in a manner that's been intelligently put together, although obviously it can't even begin to put you through the same emotional trauma as the original did. Their first good decision is not to go for the comedy. We begin with a heartfelt flashback scene from episode 24, in which Kyoko is discussing with her parents and father-in-law whether or not to take back her old name and forget her dead husband... while they're visiting his grave. Even just that first scene is surprisingly emotional, actually.
After that, we're into a chronological trip through the episodes. They're careful to include everyone's introductory episodes so we always know who everyone is, so we've got Godai, Ichinose, Yotsuya, Akemi and Akemi's see-through nightdress (episode 1), Mitaka (episodes 8-9), Kozue (episode 12), Yagami (episode 53) and Asuna (episode 56). That's a lot of supporting characters, especially for ninety minutes, but they're juggled exceptionally well if you don't mind having to read between the lines to guess how their stories eventually work out. Yagami is given a good-sized but self-contained chunk of the film, for instance, and doesn't appear outside it. Her only episode after her introduction is episode 66, but it's a good one in which we see her going typically over the top. She says some extreme things to Kyoko in the Cha-Cha-Maru, reaches some startlingly far-sighted (if judgemental) assessments and then tops it all off with something very Yagami-like. It looks (and is) weird and hostile, but in its own way it's almost a vote of support.
Then there's Mitaka's anti-Yagami, Asuna, who even gets some chronological reshuffling to separate her story from other people's. Her omiai introduction in episode 56 is split into in two chunks, one on each side of episode 66. After that we're straight into episodes 83-85, in which we get open sexual invitations, Godai-Mitaka comedy and Asuna coming out of nowhere to break your heart.
We're into the final stretch now of episodes 91-93, followed by a whole ten minutes of episode 96. Kozue's important here, which is slightly unfortunate for the film since she was introduced very early in the series and yet there hasn't been any time for us to get to know her since then. It's not a crippling problem, but it might have been if the film hadn't been so deliberate in its use of Yagami, Asuna and even Mitaka. Meanwhile Akemi does something appalling, although she says it's for a good reason, and the Godai-Kyoko relationship at last comes to a head. This is the part where the film was never going to be able to measure up to the TV series. These scenes were never going to have the same force without that 93-episode build-up. Here we've merely been waiting to see them. The TV series had us screaming for them. If you're familiar with the original, I suspect your emotions here will be partly due to your memories, but they're still good scenes. Besides, the finale with Kyoko and Godai saying goodbye to Souichiro's grave from episode 96 remains as good as ever.
The second OVA, Shipwrecked on Ikkoku Island, is both the funniest and the most lightweight of the three. It's just another episode, basically. It doesn't change anything or shed any new light on any of the story arcs, although it does provide yet more evidence that Akemi, Ichinose and especially Yotsuya are evil. There's a framing story in which Yotsuya is shown to be just as malevolent as he is in the main plot, but in a completely different way. Anyway, the main plot. Everyone from the Ikkoku boarding house is partying on Mitaka's boat, since he'd made the mistake of inviting Kyoko on there and so inevitably all the others invited themselves too. There's a clue as to what happens next in the title.
Godai's being even moodier than usual. Meanwhile his ongoing rivalry with Mitaka is as always pathetically childish and very funny, not helped by the fact that even on a desert island he's still a failure at pretty much everything he does, despite the fact that of course he's trying his best. However Mitaka as usual is terrified of Kyoko's dog to the point of idiocy, so that's the two of them reduced to the level of pre-schoolers. This episode isn't in any way a must-see, but it's entertaining.
The third and final OVA, When the Cherry Blossoms Return in the Spring, can be imagined as the Maison Ikkoku equivalent of Babylon 5: In the Beginning. You'll remember that Babylon 5 had all this backstory about the Earth-Minbari war, which was fundamental to understanding the series and yet we only ever glimpsed in flashback. Eventually JMS went back, took all those flashbacks and turned them into a TV movie. The Maison Ikkoku equivalent of this is the story of Kyoko's late husband, Souichiro. We never met him in the show. He'd died before the first episode, leaving Kyoko a widow, but Kyoko's memories of him cast a long shadow that took everyone years to come to terms with. She really loved him. Here we see that.
This could have gone in all kinds of directions, but in fact it's lovely. The footage may be familiar, but they've added narration from Kyoko herself which ties it all together and makes it feel like a single coherent story. The main oddity is that the series never let Godai learn what his deceased rival Souichiro had looked like until the very last episode, e.g. with photos having been damaged, so quite often these TV clips will show Souichiro's head and/or upper body in silhouette. Not always, mind you, but sometimes. Furthermore there's deliberately been no attempt to make this look naturalistic, so for instance he'll have a black blob for a head while walking through the playground. This is a bit disconcerting and to a newbie it would probably look weird and inexplicable, but to be honest it's just one of those things.
It can even be funny, in a gently understated way. There are laughs to be had from Kyoko chasing after him while she's still a schoolgirl and he's a teacher, for instance, although both marriage and then widowhood come surprisingly early. The last third of the OVA is about what comes afterwards and how Kyoko copes with it. Their married life together only lasted six months, you know. It's melancholy, but it never wallows in grief and it ends on an optimistic note with Godai and Kyoko meeting for the first time in episode one of the TV series. Actually, I thought it was beautiful.
Overall, I liked these a lot. Shipwrecked on Ikkoku Island is fine. I don't adore it, but it entertained me and it's a good episode. It would also have been wrong not to have a comedy in there, whereas the two compilation OVAs are surprisingly heartfelt and more rewarding than I'd expected of clip shows. I'm glad I watched them. Incidentally the odd scene gets repeated in both, but that's unimportant. Admittedly these OVAs don't have the cumulative power of the full series and they're in no way a substitute for it, but they're good additions.