Actually 3 random encounters, a party of 3 hunters will run by you, yelling at their prey. If you follow them and engage in dialogue, they will offer to sell you some strange meat. At this point, anyone who has completed the Anadale quest knows exactly what is going down, but to a new player, the offer is tempting, the meat is cheap, and they even will give you free samples. However, if you ask them about the origin of their delicious kebabs, they will dodge around the answer, telling you that it is simply "the best kind around." Its only that if you follow them as they stalk their prey that you find out that the game they hunt is the most dangerous game of all. No, not Deathclaws covered in cazadors - we're talking human beings. Those delicious chunks of meat you wolfed down don't seem so appetizing now, do they?
Actually maybe they do. After you start drinking out of irradiated toilets, pretty much anything would top that.
A quest based encounter, if you finish the Wasteland Survival Guide for Moira Brown (assuming you didn't kill her the moment you heard her speak), at some point or another you will find a Wastelander hunting a Mole Rat (Radscorpion, Mirelurk or Raider if you did all of the bonus objectives) and if they survive, he will approach you and ask if you are the author of the book. Depending on how well researched the book is, if you reply "yes" they will either: attack you, claiming that it got their friend killed (no objectives researched); give you a word of thanks and move along (basic objectives researched); or give you a reward for all the help the guide has given them (secondary objectives researched).
See, maybe it's worth it to try a little and not just troll poor Moira with bad information? I mean, you could certainly use the good karma, since you'll inevitably blow up Moira's entire town at some point anyhow.
A simple yet terrifying encounter, simply because we can all relate: you find a Wastelander being stalked by a wounded Deathclaw. Do I seriously need to explain any more? Anyone who has played the game knows that Deathclaws are the ultimate assholes, and scary as hell to boot. Even a crippled one can still wipe out your whole party in a few arm swings, and a poor unarmed Wastelander wouldn't have a chance against one. If you follow, the Deathclaw will kill the Wastelander, and if you kill the monster, you will find the schematics for the Deathclaw Gauntlet on the human's corpse. Now that Wastelander can go to his grave peacefully, knowing he did some good in the world by giving you a cool new weapon to murder doctors with so you can loot their corpses for meds.
Perhaps the most surreal of the random encounters, if you chose to expel the residents of Vault 101 after the events of Trouble on the Homefront, there is a chance that you will stumble upon this event. You witness your old childhood pal Amata getting interrogated by two Enclave soldiers and an officer, demanding to know where she got her Pip-Boy, and the exact location of her Vault. After giving up the information, the officer commands the soldiers to open fire, and you get to watch as your lifelong friend crumples into a lifeless heap in the irradiated dust. If you try to come to her aid, after killing the Enclave soldiers, she will simply shout at you to go away, that this is all your fault. Actions have consequences, and this encounter will more than likely make you rethink a lot of the choices you had made in the game up to that point. Then, after you've taken stock of your ethically-challenged path, you can go right back to robbing everyone in sight while singing along to old timey radio music.
Yes, you read the title right, no the screenshot is not a mod. The Super Mutant Philosopher, named Uncle Leo, can be found wandering the wastes, spreading a message of peace. If you try to rob him, he will give you a suit of pre-war businesswear and express his sadness that he cannot give you more (a reference to a Zen Buddhist koan). He refuses to enter combat, and will flee if you attack him. However, if you choose to be friendly and converse wih him, he will give you insight into the creation of the Super Mutants in the Capital Wasteland (for example, he comes from a "a cold, dark, metal place") and then wish you farewell.
You can encounter him a second and third time, the second of which he tells you the story about how he fell into an old basement and found a stash of purified water. The third time if you express your concern that the Capital Wasteland is too harsh a place for him, he responds with this "You may be right. Most people I meet seem to feel the same way. I used to carry around much anger about my past, and fear about what would happen to me next. But it became so heavy I was not able to take even a single step. So I had to put it all down. It may be that I'm just not as strong as most people. I will have to think on these things." Pretty deep. Sometimes you can learn something, even from a hideously mutated human from a video game.
And, if you've been paying attention to Bethesda's output over the years, you'll notice that Uncle Leo shares a name with a certain friendly zombie from The Elder Scrolls: Oblivion (the Shivering Isles expansion, to be exact). Yep, Uncle Leo (zombie-version) is also from a race that's almost universally hostile to the player, but is a lot more peaceful - just like Fallout's resident mutated philosopher. And both share a name with a character from Seinfeld!
Because including easter eggs...including easter eggs never changes.