Let's get started with Comissar Yarrick, after a great, bloody battle of Armageddon. Some would say he stood stoically over the bodies of his comrades. Those who know him would say he wept.
On the fanfic side of things, a little-known fanfic known as 'The Ballad of Gav and Bob' follows the adventures of two lovable Ogryns named... Gav and Bob. The fanfic starts out as almost the cutest thing the 40K universe has ever spawned, with Gav (our protagonist) talking about peeling potatoes with his best friend Bob, fighting 'pants stealers' and 'metal heads', and how he just loves the Emperor so huggy muggy much. Things take a turn for the tragic when an Ork sniper kills their handler, Commissar Arry. This is bad enough, but later Bob gets burned down by a pack of Tzeentchian Pink Horrors. The entire fic can be found on 1d4chan and it is guaranteed to bring a tear to even the most grizzled veteran's eye.
In general, 40K and especially the Imperium lends itself to TearJerkers; this editor feels it's the emphasis on duty, self-sacrifice, and cameraderie. You do not give up, you do not surrender, you will fight and you will die standing that others may live free. Or as free as it ever gets in 40K, but that's neither here nor there.
This Troper once DMd a GURPS game set in Warhammer 40,000 that had its fair share of these, most notably the death of the captain of the starship assigned to aid the players (one of which was an Inquisitor by that point). An acolyte opened the door into his prison cell, and closes it with a sick look on his face, not allowing anyone else to look inside.
The Imperial Guard: "We do what we do best, We die standing." Remember that they are normal humans in this darkest of settings.
Captain Blane from Gaunt's Ghosts really deserves his own entry. Tasked with the rearguard to protect against a rumoured attack by supposedly friendly units with an axe to grind against the regiment, Blane finds himself and fifty men under his command locked in battle with a far superior (in numbers and equipment) force from a rival (but supposedly allied!) unit. Fighting to the last man, Blane manages to hold them off long enough for the rest of the unit to get to safety. The most tearjerking part is that the rest of the unit had already gone on ahead, so would have no idea how hard and how long Blane's men fought, and how many traitorous scum they managed to kill before being overwhelmed.
The fate of Isha, the Eldar goddess of healing. When Slaanesh was created, he took Isha captive. Eventually, her cries for help were heard by none other than Nurgle and, being an affable sort of chap, he took pity on her and waged a massive war in the Warp against Slaanesh. Eventually he succeeded in "rescuing" Isha, and now he keeps her as a beloved companion. However, this is still the Chaos God of disease and corruption we're talking about, so he likes to show her his affection by brewing up new diseases and testing them out on her, seeing how long it takes her super-powered godly immune system to overcome them. It is a typical Tear Jerker for 40K: horrifying, sickening, and thoroughly heart-breaking.
A short passage in the High Elves fluff about a regiment of spearmen that held the pass at Tor Yvresse against an entire goblin horde, with about a dozen surviving when Eltharion finally broke through to reinforce them.
Promethean: The Created is powered by this. You are born an unnatural horror, woven from the corpses of dead men. Nature rejects you, cursing wherever you are with desolation and misery. Humanity rejects you, giving you nothing but hatred and scorn. Even the divine fire within you flares up, drawing the attention of aberrant, failed monsters that were created to be your kind, but now seek to feed on you. In your journey doubt will take you away from your path. Embracing inborn monstrosity will become more attractive than anything else. Most of the time, you will not know what it means to have a friend, much less a lover. Every moment of your existence is miserable... But why do you persist? To follow your quest, to accomplish your Great Work — to become merely human. It's a definite tear jerker, though it can be either a heartbreaking one or a heartwarming one.
The Exodus of Alexandr Kerensky and the Star League Defense Force in BattleTech. It's quite depressing to read about these men and women, forever leaving behind the remnants of the Star League they dedicated their lives to, knowing that their hard-fought battle to liberate it from an Evil Chancellor has been for naught thanks to the convoluted politics of the Successor States trying to fill the power void left by the war.
The House Steiner sourcebook mentions the wife of one of Kerensky's aides who loved her homeworld in the Lyran Commonwealth and her husband equally greatly. When Kerensky's Exodus came, she was torn between her home and her husband. She ultimately chose to join the Exodus, but her decision came too late and she arrived at the spaceport just in time to see the ship carrying her husband leave forever. Take a guess as to what she eventually does.
The short story "Requiem" from the FedCom Civil War sourcebook. It revolves around a Lyran lieutenant squaring off against a Davion MechWarrior. After the Davion 'Mech brings down several of the Lyran lieutenant's lancemates, he finally manages to kill his opponent. And then finds out that the enemy MechWarrior he just killed was his own son.
/tg/ sometimes comes up with little gems like these:
The PCs find an abandoned tower crumbling from age. Upon entering the top room they find it warmly lit by a cozy fire and a family relaxing together. The children, two little boys, are playing with toys and the youngest girl is sitting on her mother's lap by the fire. And sitting in an armchair next to them is a skeleton that the little girl repeatedly asks, "Daddy, can you tell me another story?". The entire room is a permanent persistent image of a family and inspection of the adjacent plot shows four graves, carefully tended to.
On winter nights, a beggar child comes by the local shops, asking for firewood. She always says that she is too poor to pay, that she is sorry to ask, but it is so, so cold. The shopkeepers always give her one small, specially prepared bundle of twigs each. They always say the same thing when she appears: "It's not much, but take it. Would that I had given it to you yesterday." On winter mornings at sunrise, the shopkeepers travel together to the cemetery. They all visit the same small, unmarked grave to pick up their bundles and ready themselves for the night, over and over again.