Annie, Ryze, Brand. These heroes generally take mid, because:
Ashe, Caitlyn, Graves, Trynd, etc.
Soraka, Sona, Taric. They duo bot with the AD carry.
Amumu, Rammus, Shen. Generally speaking, they jungle.
Irelia, Yorick, Lee Sin. These folks usually solo top.
This is the only list of characters by you I could find in the last like 7 pages, so I'll roll with this. If it isn't the right list though, then someone will just have to find it for me >.>
Annie, Ryze, Brand.
Annie is more-or-less tied with Ryze for shortest range of these three. Ryze is much more of a sustained caster with low spell cooldowns naturally and via his passive, and Brand is longer ranged and combo oriented via how his spells apply additional effects to targets that have his passive applied.
Ashe, Caitlyn, Graves, Trynd, etc.
Covered Cait vs Graves, but Ashe is more designed to kite (via cone aoe damage, toggle slow on attack, and global stun ult). Tryn is a melee hypercarry with a kit that does everything :rolleyes: (seriously, he has a dash, heal, slow, AD debuff, invulnerablility ult...) who is reliant on farm to be strong.
Soraka, Sona, Taric. They duo bot with the AD carry.
Soraka is the most passive of supports, featuring 2 heals and a mana recovery. She also has a silence. Sona is more aggressive, with a versatile passive, a decent heal, and strong poke as well as an AoE stun (more or less) ult. Taric is more of an anti-AD support, with a single target stun, armor aura, heal, and ally/self buff ult.
Amumu, Rammus, Shen. Generally speaking, they jungle.
Amumu is a magic damage based tank designed for team lockdown, with a massive AoE snare/attack disabler ult, percentage damage AoE toggle, aoe nuke, and reverse pull for initiation. Rammus is anti-AD and is best at locking down a single target, as well as pushing thanks to an AoE DoT ult that deals damage to towers. Shen is, well he's a bit underpowered ATM, but his strength is split pushing through a global TP ult and he also has an AoE taunt to give his team time to burst someone down.
Irelia, Yorick, Lee Sin. These folks usually solo top.
Irelia is a strong duelist, having a stun when she's lower health than her target, strong gap closer, line skillshot ult with heal, and true damage for AAs active + passive flat heal per attack. Yorick is high sustain and heavily minion based, designed primarily to win his lanes through sheer durability and all around strength. Lee Sin is very mobile and designed to bounce around the battlefield with 2 dash skills.
I just kind of wish that there were more 'signature' abilities in the game. I've stated this before, but a lot of the abilities in Riot's heroes are recycled, plain and simple (Just like a majority of the posts/arguments in this thread, though as it goes on, the rhetoric seems to get louder and more obnoxious).
Yeah, that would be nice, but even among the "recycled" heroes we have so far each plays fairly differently from any character that they "borrowed" from.
Don't get me wrong, there are aspects of League that I prefer over DotA. There's more chance for a comeback, it's less carry centric, there are scaling mage type heroes, less stalemating, and it has a somewhat less douchbaggy community- though League's is still pretty terrible. But the kits of Dota heroes are just a breath of fresh air to me.
You're one of the much more reasonable people I've replied to for the most part; i'm just getting frustrated at what seems to be a "lol sucks/lol hero design sucks" dota fanboy group that's growing here. I already can't reasonably converse on the LoL forums, and I don't wanna lose this thread...
Ok, I am willing to hear about how heroes are similar in one role in LoL, but I'd like someone to do a comparison between heroes as the post above does. Gangplank, Shyvanna, and Volibear are all bruisers (replace Gangplank with Renekton if you prefer), so they should be perfect for comparison. Or, if you want to compare mages instead, do Veigar, Cassiopeia, and Swain instead.
Let's be completely fair here: you can pick the four most different champs of any role and say
I have found the one exception, check and mate.

but there are 91 champs, and probably a lot more are similar than are different.
Btw, it goes both ways: you can't say "all the heroes in lol are boring and unoriginal" and not only ignore how the specific kit combos produce a different character, but forget how a good percentage really ARE unique and have a lot of flavor...