Please note that this answer is impossible to nail down, and with new champions being added at a rate of 1 every 2 weeks, on top of the meta shifting ever so slightly every few months, it's impossible to put together a comprehensive all-encompassing list. Factors like Region (EU vs. NA), ELO brackets, 5 man team compositions, FOTM picks, and personal bias all have a distinct effect on these picks.
I realize this question is old, but I feel compelled to expand upon some points here.
Note that these points are strongly tied in with the North American metagame, which revolves highly around 5v5 teamfights and lane pushing. The Euro servers have a slightly different mentality to them, and thus these may not apply there.
Being able to get to and from fights, as well as escape when low / from ganks is important. Characters with built in escapes like Shaco, Kassadin and Ahri are all examples of high mobility champions. The inability to gank these characters early-mid to mid game as well as the inability to finish them off in a teamfight without solid CC gives them a distinct presence advantage.
This is fairly broad, but characters that change how you lane can be strong options for bans at times. Ults with long range like Nocturne, Pantheon, Twisted Fate, Ziggs, or pure global ults like Gangplank, Soraka and Karthus all drastically affect how aggressive you can be in lane once those champions hit 6. This can be especially devastating for a bottom lane who is generally reliant on a strong CS .
Characters that are designed to force teamfights can often turn tides of the game by controlling when and where fights happen. Rammus, Galio, Maokai, Morgana, Amumu are all examples of strong initators (though not necessarily all ban-worthy for various reasons). These champs tend to be fairly durable as well, to survive the initial punishment they receive for forcing a fight. This doesn't necessarily have to be the case though. Sona, for example, is incredibly frail but can do an amazing job of initiating with a well placed ult.
Strong Snowball Champs
Snowball champs refer to the ability to jump farther ahead than everyone else in terms of damage/ability once they get even a little bit in front of the competition. Characters with scaling and spammable abilities, true damage, sustainability and steroids will often fall into this category. AD carries tend to fall in here, some more than others. You'll also see chain-casters (Ryze, Cassiopeia, Karthus, Vlad) and bruisers with natural damage boosts (Irelia, Lee Sin) in this category.