These are all the couples I support in every Digimon season up to season 4, as I haven't watched any of season 5 yet. I intend to over the summer, but not right now. I do love this series though, just like I do these couples. Please note that I am using the names from the American Dub. I do know most of the Japanese names though.
Seasons 1 and 2
Since the first two seasons have characters continuing to appear from one set of episodes to the other, I will put these in the same group of couples.
T.K. & Kari

I gotta say, these two were the very first couple I've ever supported, in fact, if it weren't for T.K. & Kari, I probably wouldn't support any couples, I would just watch shows for the entertainment value. But enough of that.. I think that my Best Friend Love basis supports the evidence for these two. I find this type of romance to be one of my favorites, & I think these two just work great for each other. I do actually respect most supporters of Davis & Kari together though.
Patamon & Gatomon

Where Takari were my first couple, these two were my second one. I've always had Gatomon as my fave digimon, & I think she & Patamon would be a pretty cool couple if they happened. I also love the fact their Ultimate/Champion forms seem to compliment each other too: Angemon & Angewoman. I think that's evidence enough. Like above though, I do respect supporters of Gatomon & Veemon. I'll never ship either Dakari or VeeGato, but I respect them.
Matt & Sora

I know some people still support her with Tai, & I can see why they would, but I think Matt with Sora won me over in the longrun after I was introduced to TV show couples. I used to support this by default; where I had seen the "25 years later" segment at the end of season 2. But I watched the whole two seasons again after starting to like TV romance, & I still enjoyed them, so yeah. Tai is one of my fave characters, yes, but I just like this couple, alright?
Ken & Yolei

Like above I originally supported this one by default too. But Ken & Yolei won me over the second time around as well, so I'll always support them. I respect Ken's fangirls of course, but I still will always support this couple.
Hawkmon & Biyomon

I'm not too big a supporter here, but I do think its cute. Plus their both bird type digimon, so its the only one for these two that seem to make sense.
Cody & Noriko

This one sort of came to me on its own. I like the same age factor, plus their personalities seem to say they'd get along well, from what we've seen of Noriko near the end of season 2.
Joe & Jun

Now this one I didn't latch onto right away, but I saw it in a Next Generation fanfic & decided that I liked the idea. No, I'm not too fond of June, but she is okay once you get past the Matt fangirl thing. I sometimes like Joe & Mimi, but for husband & wife level? I prefer him with Jun, I'm pretty sure.
That's about it for the Digimon Adventure series.
Season 3
Takato & Jeri

Now Takato & Jeri are one of my favorite Digimon couples after Takari & PataGato. I love their whole story, & how they just seem to connect easy. Plus the personalities seem to blend perfectly to me. They're one of those "natural" couples that just fall into place.
Rika & Ryo

I've said it before, I'll say it again: I'm not usually fond of love/hate couples. Usually, but this one caught my eye & I managed to like it somewhat. Plus they look good together. But I think they won't get anywhere near happening until college, if anything.
Terriermon & Lopmon

Huh, at first I thought Terriermon & Lopmon were siblings, go figure. Once I realized they weren't though, I really liked the idea. Its sort of a "fun" couple for me.
Mako & Susie

Now obviously I don't expect this to happen anytime soon in the series were this season to continue. But maybe ten or so years later, then I like the idea. However, I do NOT see this in the same way people see the Remy & Trixie idea from Fairly Odd Parents. I hate that pairing, & I just think Mako & Susie might be cute together later on, so why not? Its not like they have other potential couple ideas ya'know. Save for Original Characters of course.
Season 4
Kouji & Zoe

With only one girl human in this season, there can't be too many couples to support. I only like two, as a matter of fact. I do like J.P.'s attempts, they are pretty cute sometimes yes, but I just like the overall appeal of her with Kouji more.
Seraphimon & Ophanimon
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If you pay attention to when Ophanimon explains to the digidestined about the details of Seraphimon's capture, this couple is very obvious. She even starts to cry in the last part of the flashback when the enemy digimon start to come for Seraphimon.
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Well, those are my favorite Digimon couples, pretty long huh? This is part of why I decided on making this site, so I wouldn't have to make my DA journal so long.