Crushes
It's probably quite obvious that there are lots of people who like each other in Digimon. Try these.
Kari <=> T.K. (Takari)
This is known as "Takari", and is the most popular pairing over all seasons of Digimon. Kari and T.K. actually do admit they like each other. It occurs in S2, Ep.13, "His Master's Voice". And it's easy to see that anyway, since Kari is always sticking up for T.K. when Davis is being stupid. (Then again, Davis is almost always stupid. I'm not a Davis-basher or anything, but surely you can see that? It's because he is too impetuous and jumps out with things before he thinks.)
Davis => Kari (Daikari)
Davis has the biggest crush on Kari! He agrees with everything she says and gets really mad when she starts agreeing with T.K. instead of him. He calls T.K. all sorts of weird things (T.J., T.A., J.B. etc.) because he's jealous. He really does know T.K.'s real name. I think. He's always trying to impress Kari, for example when he gets Veemon to digivolve to ExVeemon.
Tai <=> Sora (Taiora)
In Digimon: The Movie (part 2), Sora and Tai prove that they like each other. Tai's mad because Sora's going to read his email, and then he's mad because she's not going to read it. Sora's annoyed because Tai didn't email her, and when the email goes through she says he's "stupid" because it says "Love, Tai". Also, in the third part of DtM, Kari says "Sora's still waiting for Tai to call".
June => Matt (Junato)
June, Davis' sister, is always running around after Matt. He doesn't show the same interest in her XD.
Matt <=> Sora (Sorato)
I really don't think this one makes much sense, but it's implied in S2. A lot. But if this is the case, why does Kari say Sora likes Tai in DtM, part 3? But they do get married. Which I think is just, well, wrong. Ryuko_Hikaru has a theory on this one here.
Mimi <=> Joe (Jyoumi / Mimou)
Mimi and Joe spend a lot of time together, talking. It's just kind of obvious that they like each other.
Takato <=> Jeri (Jerato)
It's obvious...
Rika <=> Ryo (Ryuki)
Rika and Ryo act tough around one another, but they're really just trying to impress each other.
J.P. => Zoe (Junzumi)
This one's obvious.
Zoe => Takuya (Takumi)
So's this one.
Kouji => Zoe (Kozumi)
This one isn't such a big one but it has a strong fan-following. Kouji seems to do little things for Zoe, like offering her his jacket.