Just want to throw this out there for people who are trying to push hard to get to Gold but feel like they're being held back by teammates. I used to get pretty mad at my teammates, and I blamed them hard for losing because "I won my lane," or "I was 5-0-0 and my team was 5-20." It took lots of harsh (but polite) criticism from GAF to make me shut up about it and fix my play.
There are two types of big games you can personally have. 1. Carrying, and 2. Snowballing. There's a huge difference between the two.
Snowballing
First, let's talk snowballing. Snowballing is when you get an advantage in lane and you push that advantage to the point where you're essentially an unstoppable killing machine. Nobody can handle you 1v1, and most of the time they'll be afraid of a 2v1 fight as well. You have a full item or two advantage over anybody, and your damage/tankiness level is unmatched. Basically you're a terror on the battlefield, but it doesn't mean that you're going to win the game, because you're just one lane that got an advantage.
You can snowball, but your team might either suffer because you've hogged kills, have ignored objectives to increase your snowball potential, or you've failed to do anything constructive with your lead. When you do make something great out of your advantage, you start...
Carrying.
Carrying is where you're playing so well that you make up for the deficiencies in your team so well that you essentially carry them across the finish line to victory. You might have terrible teammates, but it doesn't matter because you're that much better in this match than anybody else playing. People might snowball, but to carry, they need to use that advantage to push their teammates to an advantage as well or make it easy for the team to take objectives while thwarting the enemy team's efforts.
If you lost, you didn't carry, you snowballed.
If you want to start carrying, start using your advantage to benefit the team, not just to rack up kills. Kills are fun, and you can have an awesome KDA, but that's no good if you're going let your team lose. Buy more wards, frustrate the enemy jungler, roam, push lanes to force the other team to defend in more than one area, position correctly in team fights, and again, BUY MORE WARDS. Even if your team is bad, the extra vision will keep them out of trouble when you're not around. It's hard, but do it.
Given that, sometimes it's not possible to carry a team because they're simply that terrible or you get an AFK teammate or something. That happens. Even if you're truly much better than everybody in the game, you can't always carry.
Also, be wary of high snowball potential champions that suck late game unless you're confident that you can end the game quickly based on the strength of you getting ahead. I play a lot of Katarina, and I know that the longer the match goes the harder it gets. Feel free to play those champs, but you gotta start pushing objectives as soon as it's safe to roam from your lane.