My two best champions that I turn to when I'm on a losing streak or just wanna get a surefire win are Talon and Xerath, both solomid. Here's why:

Talon, amazing in solo que. With the new tiamat active and heal and the tiamat passive itself and black cleaver have increased his S3 viability. In addition to his viability, he is just all around fun to play, you can burst down almost anyone you feel like (just be prepared to die should you dive through enemy lines to destroy the ADC, which I do all the time) and you can melt teams down to around 1/2 health with your AoE burst and then can just wait around stealthed until you decide it's safe to go back in and try to pick up some stragglers. Just remember to roam around during laning phase and destroy that bot lane, it'll help your teammies do far better in the end. Also, you might not want to play Talon if your top lane is AD, makes lategame that much harder due to enemy itemization.

Xerath, stand behind your minions (allied champions) and fire from afar. Build CDR AP and blast as many enemies as you can before your meatshields die out, then simply back up. Maxed out Cdr puts his snipe skill on a 3 second cooldown and his ult on a 40 second. Mejais is viable on him due to never being in harms way. However, if your team is so scrubby that they don't even group up for teamfights, then you are screwed because you heavily rely on distance fighting utilizing meatshields. *Requires some aiming and prediction skills and a "stand back and play safe" mindset*

Definitely Zyra and Cassiopeia if you're good with them! I do mostly play Nidalee and Akali though. Much harder to carry with those, but I just like playing them so w/e!

Nunu/Caitlyn

AP Yi

Renekton?

AP Mid Taric. Obviously.

A champ that can almost always be a solid carry if you are skilled with them and are able to get your items would be ones like Leona (high cc can allow for your team to get some vital hits in, tankiness for survival, and decent solo damage), Volibear (good volibear can handle just about anyone), AP Yi (ult, alpha strike spam), Warwick, and maybe even Amumu

The fat and powerful Cho'Gath will eat their team. Or sell the ap and backdoor if he needs to.