Extremely Mixed Feelings
League of Legends is a mix of good ideas and bad implementation. As a DoTA clone, it starts with a fairly solid core gameplay involving mindless units charging toward their doom while you pick them off and gain XP and gold for doing it. Eventually, your tear down your opponent's defensive turrets and destroy their nexus, ending the game.
What's good about League is the variety of heroes available, and the fact that it's free to play and you can (eventually) unlock all the heroes using free Influence Points (IP) earned by playing the game, and each week different heroes are available without being unlocked so they can be tried out before you buy them. This variety in the heroes helps keep away boredom. The matchmaking service is also reasonably good, finding suitable matches in reasonable times and not forcing you to sit endlessly waiting for someone to join your game, and the primary way they make money is through letting you just buy heroes (instead of earning them) and through providing strictly cosmetic skins for the heroes. I also like that you can spend several games playing against computer opponents to earn IP and XP, although you earn much less than you do vs. other players.
What's bad? More than I'm comfortable recommending a game for, some of it inherent to DoTA clones and some of it unique to this version of the game. You only get gold for killing minions if you deal them the killing blow, for one, making much of the game a hunt-and-click on the almost dead minions while you otherwise stand idly by. The pace of the game is long stretches of dreariness punctuated by moments when everything happens all at once -- often 2 seconds of spamming skills determining the direction the next 15 minutes of the game is going to take. It's quite possible for a bad teammate to be worse than a teammate who is afk, since dying feeds the opponents gold and experience. I've also seen a lot of issues with connections to the server, losing about one player every other game.
The most serious offense to my strategy-gamer sensibilities is the "account level". Within each game, your heroes gain experience points, but after each game your account earns experience points as well. This account experience gives you skill points can be spent on bonuses to your hero, giving them extra armor, damage, etc. Similarly, higher level characters have more "rune slots" available for similar buffs to their stats -- did I mention that the runes also become more powerful at higher levels in addition to having more of them? This makes me particularly uncomfortable because level 30 players (the cap) can have a pretty hefty bonus over those who haven't yet grinded enough to earn those experience points, for no good game-balance reason. This isn't a matter of playing "a few quick games", but will require some serious time commitment to achieve level 30. I've played well over 20 matches (at 45 minutes each), and I'm still only level 10, to give you an idea of how long it takes to reach level 30 - and yes, the early levels came faster.
Overall, this isn't a particularly outstanding game. With the large number of other solid games out in the world, I have difficulty recommending this one. It's free-to-play, so at least I didn't lose any money on it. If you want a free DoTA clone, give this a try -- just don't expect too much.