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When Connor is mourning his friend dying from a parasitic infection. Connor tells Cutter he can't be part of the team anymore, and Cutter says they can't do the job without him, as he's one of the few people who knows the threat the anomalies pose, ignoring how two episodes earlier he fired Connor. And to cap it all, Cutter then gives him a hug.
Season 2 Episode 4 contains a pretty big Tear Jerker (it's an Anyone Can Die show, so it was very possible that Abby was actually dead), but every single thing that Connor does when he realizes she's alive is a cross between this and Crowning Moment of Awesome. Normally the Non-Action Guy on the team, Connor gets slapped across the room by a huge monster, gets back up, chases the damn thing back through an anomaly and knocks another monster out cold with a rock, all because he is not going to lose her again.
When it turned out Connor's password into the backdoor of the ARC computer system was "Abby Temple"
At the end of Season three, we have this wonderful conversation between Connor and Abby as they are stuck up a tree in the Cretaceous era with no hope of rescue:
Abby: Close your eyes, imagine a happy place, you are on a beautiful beach with the sun shining.
Connor: Are you there too?
Abby: If you like.
Connor: Are you wearing a bikini?
Abby: Yes, if you like.
Connor: The water is really warm, it is lovely.
Connor: Abby, can I move back into the flat please?
They have no hope of rescue at this point, and it isn't the way they reassure each other, it is Connor asking if he can move back into the apartment in the full knowledge that they are unlikely to ever get back home that makes this troper break out in tears.
Lester's reaction to the return of Connor and Abby in series 4, for several reasons. Firstly, he kept their lockers! Secondly, his expression when Connor and Abby come through the anomaly. And thirdly...
Lester gets another one in series 4, episode 4, when he saves the creatures from death at the hands of Burton, referencing the fact that the mammoth once saved his life.
When he finds Connor and Abby outside of the anomaly and the ensuing group hug
Becker: "I hope you brought me a souvenir"
Abby proposing to Connor at the end of series 5.
Lester furiously demanding Cutter get an ambulance even though he's already dead at the end of Season 3 episode 3.
Abby and Connor at the end of the Series 4 premiere, still recovering from what happened in the Cretaceous, but still very much in love with each other.
Lester's interactions with Jess. Yes, he snarks at her. Yes, he's just as much of a jerk towards her. But notice that she very often gets away with snarking at him where no one else could, and actually manages to slap his hand away from her keyboard without getting more than a mild "you know you could be replaced." While calming her down in 5x05:
Lester: Jess, look at me. Jess. You are the hub of this operation. You may not get the credit you deserve, but you do a brilliant job, and if anyone can pull us through this, you can.
Jess: That's the nicest thing that you've ever said to me.
Lester: I think it's actually the nicest thing I've ever said to anyone, including my wife.
Jess: Do you mean it?
Lester: Every word.
After his 10-Minute Retirement in season 3, Lester gets a standing ovation from the entire ARC staff. What makes it even better is the look on his face. He actually seems genuinely surprised that his staff likes him that much.
In the spin-off novel, Fire and Water, Lester defends Cutter's memory and his theories on the timeline after the Big Bad denounces him as a madman.