Roxolani: Good - Path of Exile
I'm rather iffy on Path of Exile myself. When I played it, everything was click-based. Attacks, moving around, talking, doing anything at all... everything required the same action of me, which made it not only boring, but very tedious, because multi-tasking was made all the harder for it (no positioning for a better attack, for instance). After a few hours, I quit, because it just had this huge barrier in front of all of its depth that every other player has talked to me about.
When it comes to F2P games, I think when talking about the "best" here, it can be divided into two questions: "Which is the best game?" and "Which does F2P best?" The first one is the one typically talked about, because the second one is prettymuch about its economic model and how it gets money from the players, which most people don't think about--or don't like to think about.
I'm going to mostly talk about the second question here though, because I find it to be the more interesting one. It will solely cover games I personally have enough experience with and memory of that I can talk about them at length.
The majority of F2P games are either mobile, or PC online multiplayer games (typically MMOs or MOBAs). There are games that do F2P well, and as a result are often more popular than games that do F2P badly but are otherwise similar (gameplay, art style, marketing). These games tend to only require money for things that do not affect core gameplay--i.e. things that do not give players a mechanical advantage, such as cosmetic upgrades to characters--or give the players things that would otherwise be much harder to acquire.
For example, in the mobile game Jetpack Joyride, you collect coins while avoiding hazards (zappers, rockets, lasers, etc.) until you die. The coins can be spent on cosmetic upgrades (for the character or for the vehicles in the game), but also on special items that grant specific abilities or bonuses during the game. You can spend money to gain a large amount of in-game coins, thus making it easier and faster to acquire these special bonus-granting items. However, you can still get these items simply by playing for a while and gathering enough coins to buy those items.
A more well-known example is League of Legends, probably the most-played MOBA of the present. In League of Legends you can also spend money to buy things, but you can also spend in-game currency that you get from playing the game. However, the only thing you can buy with money that you can't buy with in-game currency, are cosmetic upgrades. "Runes", which boost a character's in-game abilities and are essential for the game, are all easily acquirable through in-game currency. Champions, the game's terminology for its characters, are also all capable of being purchased with in-game currency, though of course they're costly enough that it'll take a few games to save up enough to buy one. Real world money simply makes it easier to get them.
Years ago I enjoyed playing Perfect World, but then I found out that a lot of stuff has to be bought with money to be able to advance or even meaningfully contribute to a party in the game. When you can buy things with real world money that you cannot get any other way, and those things include stuff that gives you a mechanical advantage in the game, then the game is Pay-to-Win. That's simply it. A lot of people call F2P in general P2W, or any F2P game that they dislike, but the above is the pure defition of P2W. A real shame, because Perfect World was otherwise quite enjoyable, despite the combat being rather shallow.
There are also some games that are partially F2P, but later have to be paid for to continue. World of Warcraft
sort of has this, in that you don't have to pay for a subscription up until a certain level (and I've heard that they are removing/have removed the subscription entirely by now). Lord of the Rings Online is a worse version, but I have less experience with the paid parts of that game.