A durable, initiating bruiser who is capable of exerting lane pressure. Bonus points if you can also jungle them for increased map presence.
When fed, Gnar, Cho'Gath, Hecarim, Jarvan IV, Kled, Malphite, Riven, Renekton, Vi, Volibear, Warwick, Wukong, Xin Zhao can dish out surprising damage, initiate and control fights, zone enemies from engaging, split-push, tank/take towers, and generally becomes a durable menace that can buy your team time to get back into the game.
They may not have the raw kill-everything power of Tryndamere/Yi/Yasuo, but their versatility and ability to make up for most issues your team can have makes them invaluable anchor points for a team.
Second options are tanks that make fights easy for your allies (Sejuani/Amumu being the top two for AoE CC that's easy to clean up after) and split-pushers who REQUIRE attention (Tryndamere is probably top of the pack there, since he can and will solo towers all day if you ignore him). Note that the split-pushing strategy becomes worse and worse the more coordinated your enemy team is, and the anchor strategy becomes better and better the more your team is (as then "bad teammate" usually means "decent teammate who is having a bad day and needs an anchor to get back into the game.").