Cocaine Bear: Beth the paramedic may not be immune to Freak Out moments, but she helps the injured Liz back to the ambulance and waits for Tom to ride with them rather than abandon either of them to the bear.
Jason X: Janessa doesn't want to die and doesn't risk her neck throughout Jason's rampage (once half-sarcastically suggesting that the others fight while she runs), but she remains fairly helpful and compassionate toward the others. At one point, she pleads for a rescue ship to keep coming even after Waylander says that it won't arrive in time to do anything but risk being caught in the blast radius, but she also manages to Face Death with Dignity a few times when things seem hopeless.
Mad Max 2: The Road Warrior: The Curmudgeon wants to bargain with the marauders for safe passage rather than fight them, but he's a friendly man who carries his own weight and never tries to betray the others to save his own neck.
Bob Hope, in many of his movies. See The Princess and the Pirate, where he's a bumbling, cowardly actor who somehow saves Princess Margaret from the pirates.
Woody Allen, who admired Bob Hope's use of this trope, plays the same type of character in many of his early films.
A Slight Case of Murder: Dick is an honest police officer and a loving fiancee to Mary, but the final scene shows he's not very brave. When he's Framed for Heroism by being sent after four criminals hiding upstairs (who are already dead), Dick initially wants to just stand guard at the stairs until more cops arrive. This makes some sense, as reinforcements are only about two minutes away and he's badly outnumbered and woefully inexperienced. When everyone persuades him to shoot it out with them, Dick can't even look in the direction where he's firing, and Marco has to hold his arm steady for him. Then, once he's emptied his gun, Dick faints.
Monty Python and the Holy Grail has Sir Robin, the Not-Quite-So-Brave-As-Sir-Lancelot, who had nearly fought the Dragon of Angnor, and who had nearly stood up against the Chicken of Bristol, and who had personally wet himself at the battle of Badon Hill:
Brave Sir Robin ran away "No!" Bravely ran away away. "I didn't!" When danger reared its ugly head, he bravely turned his tail and fled "No!" Yes Brave Sir Robin turned about "I didn't!" And gallantly he chickened out. Bravely taking to his feet "I never did!" He beat a very brave retreat "All lies!" Bravest of the brave, Sir Robin! "I never!"
Jonathan from The Mummy Trilogy is more reluctant than any other cast member to engage in the very dangerous world-saving business but does not seize any opportunities to leg it and makes critical contributions. Stands opposite Dirty Coward Beni who throws the rest of the world under the bus to save his own hide.
William Moore, the President Target of Big Game prefers running and hiding to facing his opponents, and is afraid of jumping less than three metres down.
Star Wars' C-3PO. He has mild elements of Cowardly Lion in that he will run into danger after his friends, but that's as far as it goes.
Loomis in Quick Change. It's useful for the bank heist, but a terrible fault when the getaway starts to crumble.
Hoggle from Labyrinth. He even admits it, saying that it's the reason he obeys Jareth. ("I'm a coward, and Jareth scares me.") Eventually, however, he does get better.
Peter Page from The World's End is timid and easily led, not to mention he's the only one to hide during fights. This is at least partly a result of being heavily bullied as a kid.
Donatello is showing hints of this in Teenage Mutant Ninja Turtles (2014). He had an Oh, Crap! reaction to the Foot soldiers having guns and he declared that he wants to be badass for once.
In Pixels, Ludlow is completely terrified of the prospect of going to The Mothership. However, he stays rather heroic on the ground.
The Commuter: Jimmy doesn't take part in the attempt to venture outside of the train and fix int in order to prevent the crash, and is the only prominent character not to take part in the I Am Spartacus moment, but is a friendly and helpful guy overall who provides some comic relief and never makes any pretensions about being braver.
Avalanche Sharks: Carol freaks out whenever the sharks are coming after her and is the main voice against trying to rescue Dale while he is badly injured and surrounded, but she does go out into the woods looking for her cousin when she thinks something happened to him, points out why they shouldn't go after Dale sensibly (he'll just bleed to death from his wounds if they take him into the warmer hut, and there's no obvious way to get past the sharks and bring him in), and, along with Wade and Diana, does give up a good opportunity to escape by stopping to listen to Dale's pleas for help a bit later.
