Random Event: Mugger
This random event involves chasing down a petty thief after he has mugged a civilian. If you come across this event early in the game, the thief will have a higher stamina than you so it is best to chase him down in a vehicle. In fact, he carries a pistol so it is best to ram him when you can to dispatch him. He will drop the purse once you have taken him out along with his pistol. From there you can either choose to return the purse or not, it's up to you.
Reward without returning the purse: $500
Reward with returning the purse: $50
Random Event: Designated Driver
You'll come across this random event just southwest of Trevor's safehouse (just west of the barber shop). A couple here will ask you to drive them back to their hotel as they are too wasted to drive.
Get in their car nearby and they'll get in after you. Now, from here you have the option of either taking them back to their hotel *or* of taking them to the Altruist Camp in the Chiliad Wilderness (which is now marked on your map with a giant "A").
The choice is yours and really just depends on how greedy/evil you are feeling I suppose. The Altruist Camp is quite a drive but the monetary difference is quite large as well.
Reward for returning the couple to the hotel: $80
Reward for handing the couple over to the Altruists: $2000
Random Event: Cop shoot-out
Now this one is interesting. You can come across this in Harmony, at the intersection of Route 68 and Senora Road. You'll likely come across it when you are first playing as Trevor.
Basically the cops are in a shoot-out with three robbers. The reason this is notable is because the robbers actually have two briefcases on them that are worth $5,000 each, which are our primary target here. However once you grab them you will automatically get a two-star wanted level (they are police evidence after all), so be ready to lose the heat!
Random Event: Altruist Attack
While driving on Baytree Canyon Road (south of the Harmony area), you can find a woman being attacked by two altruists. They will have her down on the ground and tell you it is not your problem.
Go ahead and cap them both. The woman will thank you and ask you to drive her home (which is a short drive to the north). For being so kind and saving her, she will reward you with $80.
Random Event: Gold-Cheating Husband
While driving on Wild Oats Drive in North Vinewood (what an appropriate street name), you will come across a wife throwing all of her husband's stuff out on the lawn. Stick around and listen to the arguement. Golf at midnight? Sure...
Afterward the man will ask you for a ride. Take him in and he'll ask you to drop him off at the Los Santos Golf Club. Go ahead and do so while you have a chat with him. Turns out he is cheating, just not during his golf time so his wife is wrong (but also right...). In the end you'll get a new contact to go play golf with.
Reward: Golf Contact: Oscar
Random Event: Hitchhiking Bride
While driving on Route 68 west of Harmony (around the 68 and Zancudo Grande Valley intersection), you may come across a bride in her wedding dress asking for a ride. Pick her up and she'll confide that there's no way that she can handle being married so she wants you to drop her off at her home.
However, the husband isn't about to let her get away, as he will come chasing after her soon. The easiest way to lose him is to stop and wait for him to get out of his vehicle since you can speed away, but honestly you should just try to barely outrun him so you can listen to all of the entertaining dialog that takes place between the bride and groom. You do lose your navigation though, so how long you wish to drive like that is up to you.
After dropping her off the bride will thank you and leave. No reward money for you! What the heck!? If you are playing as Trevor, you have the choice to take her to the Altruist Camp if you wish. This is a long trip but nets you a $1,000 payment. Given the fact that she doesn't pay crap it is a very attractive option.
Random Event: Burning Wreck
While driving on Route 13 on the very north side of Blaine County, you may come across a burning wreck with a woman lying down next to the freeway! Yikes! Stop by here and help her up. She will refuse hospitals and express gratitude that you got there before the cops. That of course reeks of, well... nefarious purposes, so naturally you guys have something in common. Listen to her story and take her to her safehouse at Sandy Shores. At the end, you'll have a new heist crew member!
Reward: Heist Member Unlocked: Taliana Martinez
Random Event: Security Van Collection
While driving near Paleto Bay (which is the very north side of the island), on the southeast side of Paleto Blvd, you may find a security van stopped. The guards are nearby and are in the process of collecting.
If you wish you can shoot them down (which gives you a two-star wanted level) and collect the briefcase they were handling. This should net you a tidy sum of money ($6,000+). From this location it is easy to head south into the woods and lose the cops: just be quick about it as they are on their way.
Random Event: Lost MC Robbery
While driving in Los Santos around the Hawhick Ave and Alta Street intersection you may hear a cry for help! A business owner has just been robbed by the Lost MC. Chase the van down; try and shoot out the tires to force it to a stop. Be ready to take out two lost members once you stop the van. One of them will drop the cash they stole from the business owner: $2,000. You can choose to return this or keep it for yourself from there depending on how generous you are feeling to your fellow man at the time. If you do return it, the business owner will give you a $200 reward.
Random Event: Street Hold-Up
Turns out you aren't the only criminal in the city! While near the Hawick Avenue and Power Street intersection (or, more precise, a little east from there down the Hawick Avenue road) you may encounter a lady getting robbed at gunpoint. Here the robber shows up on your radar as a hostile. You can choose to mind your own business here or take down the robber for the lady.
If you take down the robber, she will run away (and yell something about getting you tickets), so no reward for you. The robber has a gun and some petty cash on him.