In "Carter Turns Traitor," Hogan has Carter pass for a chemical warfare expert and be taken off to a chemical plant, leading them to dress up in SS garb and masks (even Kinch) to retrieve him. Before going, Hogan reminds the men that it'll be very dangerous (in broad daylight, lots of German troops around) and therefore strictly voluntary. The boys' answers?
Given the era this is set in, the fact that Kinchloe and Baker are respected by the other prisoners definitely qualifies.
In the opening of "The Great Brinskmeyer Robbery," Kinchloe is in the tunnel when an explosion occurs; all the men scramble to get him out.
Newkirk may pick on his friends all the time but he definitely cares about them a lot. His reaction to LeBeau and Carter coming back late in "Diamonds in the Rough" says a lot. Interestingly he shows a lack of worry towards Carter's absence in "One Army At a Time" assuring the others that Carter can take care of himself. This, coming from the guy who calls him an idiot more than anyone else.
And when the tables are turned and Newkirk is captured, Hogan seems to write off the loss. The men seem on the verge of mutiny until Hogan reveals that he only acted that way to bluff a double agent who was in the room with them, and that he wasn't going to leave one of his own men behind.
LeBeau's farewell scene in "Cuisine à la Stalag 13", especially his goodbye to Newkirk. Those two have a lot of heartwarming scenes in general.
At one point, Newkirk and LeBeau are out on a job and are past due back. Kinchloe asks Hogan for his thoughts on the risk.
Hogan: Kinch, all that matters is victory. Even if you have to sacrifice two good men.
Kinch: Right. (beat) And if they're not back in ten minutes, we're going out to get them, right?
Hogan: (nods) Right!
A very quiet one in Klink's Secret Weapon. A new sergeant that Klink brought in to improve efficiency is running everyone into the ground and quoting regulations to the letter to back himself up to the point that Hogan's men have collapsed into their bunks halfway through the day. Hogan was trying to plan, but upon realizing his men are unconscious, quietly drapes a blanket over them and lets them rest.
Another nice scene (which also doubles as a Crowning Moment of Awesome) occurs in "The Flames Grow Higher". Hogan orders LeBeau and Newkirk to wait ten minutes while he checks out a potential trap and then run back to camp if he doesn't return. Ten minutes pass, Hogan isn't back. Cue Newkirk and LeBeau coming to his rescue.
LeBeau: The Colonel gave us a direct order! Return to camp.
Newkirk: (on Hogan's order to retreat) Monsieur LeBeau. If you start obeying officers, we're gonna lose this bleeding war!
General Barton saluting Hogan at the end of "The General Swap". For context, he had called Hogan a traitor earlier in the episode, regarding the lack of escapes from Stalag 13 as Hogan selling out to the enemy.
Hogan may hook up with almost every girl in this series but it's clear that he really cares about Tiger. Case in point, he disobeys direct orders from London in order to save her.
More than that, the entire crew was ready to write her off due to said orders until Hogan stated that if they wouldn't help him, he'd go alone. Carter almost immediately volunteers to help him out. Followed closely by LeBeau, Kinch, and Newkirk.
Burkhalter's Pet the Dog moments with his family count. He's not a nice guy, and he is easily one of the more dangerous adversaries the heroes (and Klink) face, but he definitely cares about his family, examples including getting a famous designer to sew a wedding dress for his niece, and attempting to marry off his widowed sister so she wouldn't be lonely anymore