Digimon Adventure is remarkable amongst children's anime for two things -- first, the spectacular and accurate rendering of Odaiba as it was in 1999, and secondly, its characterisation. To quote the TvTropes page, "we came for the monsters and stayed for the children", and when there's appreciation for characters, shipping is never too far behind. Yamato has been shipped with almost everybody at some point. Let's take a look, shall we?
Yamato + Taichi (Taito/Yamachi/Taiyama)
The big one, and the most obvious one. (And my slash OTP, no less.) These two complement each other perfectly as best friends, and as lovers I believe they'd do the same. At the height of Digimon's English fandom, Taito was insanely popular, and remains so even now despite the much smaller size of the fandom these days. There was intense Taichi/Yamato interaction in the first series, and that same intensity between the two didn't even let up in 02, where Yamato and Taichi were only secondary characters! I honestly believe there could have been something there until the whole deal with Sorato popping up apropos of nothing in the last few 02 episodes.
Yamato + Mimi (Mimato/Yamamimi)
My het OTP and the favourite pairing with the dubbies. (I didn't mean that as an insult, I started out as a dubbie myself!) Mimi and Yamato were paired together for a few reasons -- firstly, the aesthetics of the relationship are delicious, and secondly, as a sort of complement to the Taichi/Sora relationship (which was just as obvious as Taito, if not more so). It was often criticised as unrealistic because Yamato and Mimi didn't often interact. But despite this...I love Mimato, and I honestly think that Mimi and Yamato's personalities actually would mesh really, really well. But more about that on my silly fun Mimato site...^~
Yamato + Sora (Sorato/Yamora/Yamasora)
I have a lot of opinions on this pairing, and unfortunately, none of them are all that good. Yamato didn't interact all that much more than he did with Mimi, really, and suddenly, it's supposed to make perfect sense that he and Sora are suddenly so much in love they can blurt out 'aishiteru' to each other? It boggles my mind. Also, perhaps if Toei hadn't mauled Sora's character, I might have been a lot more accepting of this pairing. However, when she's around Yamato (at least in the latter parts of 02), Sora turns into someone she isn't. I don't think Sora Version 66.6 is good for Yamato, and vice versa. Keep Sora as she was originally, and it might've been sweet. (But of course, if you kept Sora as she was originally, then logic dictates she should have been with Taichi!)
Yamato + Hikari (Karato/Yakari)
Fascinating couple (big brother's best friend, yo!), but I don't see it happening. Hikari is much closer to Takeru (naturally) and even Daisuke than she is to Yamato. Plus, age gap could get a little awkward -- it can seem like a million years between 11 and 14, just not three! Plus, Taichi might kill him if Yamato touches his baby sister! ;)
Yamato + Miyako (Yamako)
Is Miyako even aware that Yamato is around...? No? No, not really. But...WHO CARES. I have a secret guilty pleasure for Yamako. I was introduced to it by an affiliate (whose amazing site was in a state of stasis when Geocities closed, but you can view it here), and this is a really creative coupling. It's fun and funky, and I think Miyako (if she manages not to drive introverted Yamato up the wall) would bring Yamato out of himself a lot.
Yamato + Jun (Yamajun/Junato)
Ah, Jun, so needlessly hated on. I think she's hilarious, myself! But anyway. Didn't she sort of get over Matt and start chasing Jyou's older bro around...? Yesh, she did. Either way, Yamato officially can't stand her. And she's now determined to become Mrs. Shuu Kido, so...^~ Jun was never a real threat, dear fangirls. Could they have made a decent couple? Probably not. Much like Miyako would, I think Jun would drive Yamato crazy, and not in a good way!
Yamato + Jyou (Yamajyou/Jyouto)
When I first came across this pairing, I thought, "No freakin' way!", but over the years, I've really warmed to the idea. There's a fair amount of Jyou and Yamato interaction in the first season (and without Jyou, Yamato's crest would never have glowed!). This can be an extremely sexy pairing, when done right...
Yamato + Koushirou (Yamashirou)
I've tried to wrap my mind around this pairing, but I find it really difficult to do so. I don't know if it's because Koushirou seems to present himself as almost asexual or what, but there you go. I haven't seen this pairing around too often, either.
Yamato + Daisuke (Yamasuke)
Well, after they got over their few differences at the beginning, I think Daisuke and Yamato got on okay. I think Daisuke respects Yamato and looks up to him, but not as much as he does with Taichi, and I can't see it in a romantic way. Oh well!
Yamato + Ken (Yamaken)
This couple is so adorable! Can't you just see Ken turning to Yamato when he's unhappy and having Yamato totally understand how he feels? It's too, too cute!
Yamato + Takeru (Yamakeru)
One of the more taboo pairings (apart from Mimato...I jest!), with good reason. This is incest, and I personally find it as squicky as hell. It was somewhat prevalent during the height of Digimon fandom, but I think Takeru only has eyes for a certain Yagami...as does his older brother :P
Iori's nine, man. I really can't see it happening until some years down the track, when Iori grows up a bit?