I'm here to talk about lane swapping, which I almost never see in ranked. I'm writing this primarily for the solo laners, where the power relationship is clearer.

Well, let's talk about the pros and cons of lane swapping first. The first con I can think of is the fact that you have to get to the other lane, which takes about twenty seconds or so. That's about the time a minion wave takes to spawn (thirty seconds), so for simplicity's sake, let's say that if you swap a lane you will lose about a minion's wave of gold and XP. XP basically becomes a non factor after level four, and six minions is about 124 gold, or basically a ward and a pot. So it's "reasonable".

Another thing you want to keep in mind is that if you swap with someone who can't handle the lane (like a Nasus into a Teemo lane), you're basically feeding your opponent, which kind of defeats the purpose of the lane. Of course, if you really need to, you can just swap into the bot lane. Sure your gonna get zoned, but you can still last hit under the tower, and it's practically guaranteed that the duo can handle the lane you give them.

But if you and your teammates can handle it, sure why not? Winning the lane is an uber important part of winning each game, each lane has an important part in teamfights and map dynamic as a whole, if the bruiser top gets super fed, you can bet that the enemy will spend a lot of time running from the 2k hp jax. Same goes for AP mid, if that Ahri gets fed, you can bet that there will be a lot of roaming, and kills for your team.

So why don't people ask for lane swaps more commonly? My personal opinion is that there is a stigma on the whole "revealing you are weak and asking for help from a stranger" thing. This is wrong. Firstly, you are not asking for help from a "stranger", you are asking for help from a "teammate". The difference between a "stranger" and a "teammate" is that your teammate wants to win the game, and will do anything within limits to improve the chances of winning the game. If this means helping you, he will do it unless he is a troll or a newbie. Report the former and try to help the latter, if you can.

However, I would like to take a stance against this "stigma". If you are weak, and you recognize that weakness and take steps to stop that weakness, that "weakness" becomes a "strength", because the enemy can no longer take advantage of that "weakness". So, ask for lane swaps more! 

To people who are winning your lane and someone asks to swap with you. I implore you to consider their request. You have a much better chance of winning, or at least drawing with that lane than a person already behind. Losing a lane means a lot worse for your chances than if there are simply two drawn lanes, so if another lane is losing and you are winning your lane, ask to swap with them!

Update: Now once you've swapped lanes you want to either get far enough ahead that you can compete against your original lane, or if you absolutely can't win your original lane, strive to keep your lanes swapped. This usually means two things: Pressuring your lane so they can't swap and being careful of ganks so that you don't lose your swapped lane two. It's not hard to understand pressuring: Just keep pushing and continually harass so that if they leave lane they'll lose the tower, and if they stay in lane they'll die. But always keep an eye out for ganks: If you lose your original lane and your swapped lane, your teammates will hate you and you will probably lose.

Also, if you are going to swap, swap EARLY, not late. If you are taking heavy harass, swap. If you are getting zoned, swap. If you have died 5 times and he is godlike, it's too late, for both you and the lane.