Keep the Pace: Keep the Pace has you race around a track littered with obstacles. The twist here is that you're not allowed to drop below a given velocity, or you'll be eliminated.
Relay — A straight port of real world relay racing into GTA Online.
Sumo — Depends on your definition of violence, really, but we feel this deserves a spot here. Sumo pits various players against one another in vehicles perched on a tall arena. Your goal is to push your enemies into the abyss.
Slipstream — Because when there is a universally hated game mechanic, you might as well give it its own mode. Driving in the drag of a vehicle in front of you gives you a speed boost, and you must hit the checkpoints the same time as your team-mate.
Deadline - Yeah, okay, this is stretching it a bit, but Deadline isn't really violent, you just, you know, blow up your opponents' bikes. While they're on them. Anyway, this is just light cycle battles from Tron, so technically no one actually dies.
Running Back — An interesting attempt to translate American Football, also known as "handegg", to GTA Online. Competing teams must get their runners into the opposing touchdown-zone while preventing the same from happening to themselves.
Join a Car Enthusiast Crew
Love cars? Love tuning cars? Love showing off your cars? Love your cars in their non-exploded, non-shot-to-bits state? Great, you're not alone! There are several crews out there focusing on vehicle-appreciation. Their members often organize car meets where you can show off your sweetest rides and check out the cars of other like-minded players in safe environments without having to fear some buffoon in a Hydra showing up to ruin the party.
Start A Taxi Service
We've documented the adventures of a player who might have been the originator of this idea. While there is some risk involved, as other players might still harass you with their disgusting violence and aggression, more often than not they'll play along after a few moments of befuddlement.
Paint your car yellow, slap a custom Taxi crew emblem on it, drive up to players and message them whether they want to go anywhere. While it might not seem like a fun activity at first glance, since this is an MMO we're talking about, shenanigans are guaranteed to ensue.
Try Solving the Mt. Chiliad Mystery
You're going to need to be a bit insane for this one, and having your own tin foil hat won't hurt. GTA 5 still presumably hides some kind of undiscovered secret easer-egg, at least is the people over at r/chiliadmystery are to be believed. Be warned though, if you jump into this, you might go full conspiracy-nut. Chemtrails, man.
Document The Lives Of NPCs
GTA 5 features one of the most detailed and vibrant open worlds in gaming to date, even though it's over three years old. For this particular activity, we suggest playing in single player, since the game world in Online is drastically watered down to offset the higher resource-draw of a multiplayer game.
Pick an NPC, any NPC really, and start following them around. PEDs in GTA 5 will do the darndest things if observed for long enough. Just faffing about in the city, following your target, you're bound to discover some odd happening or funny occurrence involving one of the many NPCs out and about.
GTA 5's NPCs and vibrant world have inspired artists for years now, with one of the most far-out projects being one that sought to use GTA 5 as proof that we ourselves, and the world around us we consider to be 'real' are just a simulation.
Grand Theft Euro Truck Simulator
While I personally see no appeal in this, apparently people like those weird trucker simulator games quite a bit. If you're one of these people, 1) what is wrong with you? and 2) you can always play the same thing in GTA Online. Grab (or steal) a semi, attach a trailer, pick an arbitrary destination at the other end of the map and make your delivery. If you want actual systems to support this kind of gameplay as well, there is a mod for that which you can use in singleplayer.
Diving
The ocean in GTA Online has been rendered in loving detail, with coral reefs, sunken wreckages and large skeletons dotting the seabed, with plenty of opportunities to explore. Most players don't tend to hang out underwater, so you're bound to have plenty of privacy while you discover what lies in the depths. You might even find some collectibles while you're there.
Wildlife Photography
You probably have had some exposure to the animals in GTA 5 if you played Trevor's hunting missions in single-player, but you can still "shoot" animals if you don't want to harm them. The high-fidelity environments, wide array of species and a built-in screenshot suite are just begging to be used for some virtual wildlife photography.
Minigames
GTA Online is full of various mini-games and side activities that are non-violent. Beyond golf and tennis, clubhouses feature darts, you can visit nightclubs or hang out in the decadent Diamond Casino.
What non-violent activities do you like most in GTA Online?