These are in no particular order.

#1: Path of Exile

Pay to Win: No

System Requirements: Low-Moderate (G3258/750 Ti tier hardware is totally sufficient, but laptop HDDs will hurt - SSD optimal.)

Platform: Steam / First-Party Client

An ARPG (think Diablo) by an indie studio out of New Zealand. Online-only which can be a pain with bad Internet connection (ping, not bandwidth - I play just fine on a 1.5 megabit/sec connection), but excellent gameplay mechanics with enough depth to last you for hundreds of hours if you find it's your cup of tea. It's balanced just at that point where it's easy to get into but difficult to master, which is quite good.

On pay-to-win: You cannot purchase any equipment with real life cash, and trading it for real life cash is explicitly forbidden. The only things you can buy for RL cash are more stash tabs and cosmetics.

#2: PlanetSide 2

Pay to Win: Low to Moderate

System Requirements: Moderate-High (Majorly CPU bound. With my 4690K and 960, the 4690K is the bottleneck. IPC is important.)

Platform: Steam / First-Party Client

The combined-arms MMOFPS that earns the "MM" part of the acronym. All combat takes place in a large, combined open world, with small and large bases at regular intervals which can be captured and moved between.

This game has a fairly steep learning curve, but when it really gets rolling, there is absolutely nothing that can match its scale - 96 players on each side is a fairly common occurrence during prime-time.

On pay-to-win: While a few specific items you can purchase with cash are plain beneficial (MANA anti-vehicle turret being one of them), there are two main points keeping it in balance: 1) the vast majority of weapons are sidegrades instead of upgrades, and the stock weapons are quite competent enough to get many kills in the right situation, and 2) the equipment upgrades (armor, mines, C4) cannot be purchased with cash.

A note: Teamwork is the most powerful weapon in PlanetSide 2, far more than any rifle or tank gun. If you've got friends, you can kick ass.

#3: Robocraft

Pay to Win: Moderate-High

System Requirements: Low-Moderate (It's a Unity game. Single thread is paramount. A G3258/750 Ti setup will do fine, but laptops might have issues.)

Platform: Steam / First-Party Client

A multiplayer PvP buildy-shooty game - you assemble a bot (or several) with a skeleton of voxel pieces and your choice of movement and weapon components, then battle it out in a few different gamemodes. It's currently in a troubled state with regards to game balance, but the construction is neat and worth a shot - cause after all, it's free!

On pay-to-win: You can straight up buy every component in the game with real-life cash, supplanting a long grind. However, the components you can buy only with cash are exclusively cosmetic, so you can't pay to get an advantage that can't be countered by regular players.

#4: Boring Man: Online Tactical Stickman Combat

Pay to Win: No

System Requirements: Very Low (It's a 2D side-perspective action combat platformer. Made with Game Maker. Just about anything can run it.)

Platform: Steam

An excellent one-man indie game with fast-paced wall-jumping platforming combat and a veritable smorgasbord of weapons. Great casual game, and it even has a level editor.

On pay-to-win: Cosmetics only. It's great.

#5: Team Fortress 2

Pay to Win: Hats (so no)

System Requirements: Low (If it has a dedicated GPU more recent than 2007, or a Haswell onward or AMD A8/A10 iGPU, it's probably good.)

Platform: Steam

I often forget this game is free-to-play now. A classic team-based shooter (how team-based depends on who you're playing with) with many different gamemodes and several subvariants, more cosmetics than you can choke a camel with, and community servers both vanilla and with a wide range of mods.

On pay-to-win: No, not really. Hats don't benefit you. And weapons can be gotten easily via random drops or trading with a friend who has TF2 (with a long-time friend, authenticatorless trading takes 1/15 of the time!).

Conclusion

There's a remarkable amount of good F2P games on PC, and I have a feeling most of you are going to be hearing about at least one of these for the very first time. I hope I've helped you find a cool new game!