Since few, if any players, will be dead set on playing in the Jungle or as a support Champion who doesn't kill any creep, those roles are typically left unfilled, as everyone tries to play to their particular style. As they might say on a never-forgotten 90's sitcom, there's absolutely nothing wrong with that.
Except that what works when you are level five is not going to pass muster once you start playing against other 30's with full Runes and Masteries.
The lanes are set up in the traditional metagame as Solo Top, AP Mid, ADC, Support, and Jungle, for a reason, and it isn't because someone randomly decided that order looked pretty.
Solo top and AP Mid get lanes to themselves in order to maximize the number of minions they can slay. This, in turn, leads to quicker acquisition of powerful items, and access to higher levels faster than they would earn if they were splitting experience. The Champions that play in those lanes tend to be reliant on their item builds and need to have high levels in order to chain their abilities together effectively.
Solo Top bruisers are designed to play by themselves, able to hold their own even in 2 on 1 gank situations. The squishy AP Mid, on the other hand, gets help from either Top or Bot Lane without too much stress caused by roaming through the river or jungle areas.
For Duo Bot Champions, they work well with a teammate. The support often uses devastating Crowd Control effects (known hereafter as "cc") to Stun, Slow, Silence, or Fear opposing Champions and help their ADC escape from sticky encounters. With a Support around, protecting them, the Carry is free to farm and focus on harassing the enemy, splitting the experience but not the gold.
The Jungler likes having a lane to him or herself, and can farm through the Neutral Minion camps fast enough to mimic playing against waves of minions. Without a successful kill early, the Jungler will normally be behind on levels, gold, and experience, but makes up for it with powerful presence during ganks.
When your team composition does not fit this traditional mold, it can have a negative effect on the laning phase of the game. Champions may become underleveled or be unable to purchase the items they need at the times that they need them. If you don't have a Jungler, the opposing team's Jungler can roam your side of the map. All while stealing buffs and ganking from unexpected positions; wreaking havoc seemingly at will.
Remember what I said about Solo Top Champions being able to handle 2 on 1s with relative comfort? If you try and go against a top lane champion like Singed or Irelia with more than one person, all you are doing is letting them farm under turret while slowly out-leveling and earning more money than you.
Keeping all of that in mind, there are unconventional strategies that some teams will adopt to attempt to beat the metagame. This is a brief list of less common set-ups and what they do. More in-depth treatment of each strategy will come later, when each is covered individually. Also, please note that some teams will experiment with the traditional five roles playing in different lanes; this is a legitimate common strategy that will appear with some frequency at higher levels, and therefore does not fall into this section.
2/1/2 -- The most common non-metagame set-up that you will encounter, usually because no one on the team feels comfortable in the Jungle. When run as an actual strategy, 2/1/2 requires either a Support player in both Top and Bot lanes so that the team is not attempting to have two Champions farming the minion waves, or a lane designed to demolish opposing Champions, earning gold through kills rather than creep (see Kill Lane).
Kill Lane -- From time to time, you will fight against or with a team that insists on having two high damage carries play alongside each other. This is known as a kill lane, as one of the carries will farm and the other will harass constantly, hoping to catch either the support or the enemy ADC out of position for an easy kill (earning them the gold and experience they are otherwise losing from not farming).
Double or Duo AP -- With two competent AP Mid players, this 1/2/2 strategy can be overpowering very quickly, resulting in a broken turret in the middle lane as early as the 3:00 or 4:00 minute mark. Once the tower is down, one of the mid Champions will start roaming, if not both, creating a rush environment that greatly speeds up the game. When done well, this is hard to counter, as the Jungler will frequently be underleveled and the opposing AP Mid will have been cut off from farming, starved by the power of the Duo AP lane.
Tri-Lane -- A very uncommon strategy that works like the Duo AP method. Designed to break a turret as fast as possible, this 3/1/1 arrangement preys on unprepared teams that send their Solo Top unwittingly to his or her doom. The three Champions that lane together usually start in the Jungle, biding their time to let the opposing Solo Top push the lane far enough that they can score a fast kill and clear the minion wave before the other Jungler can react.
ARAM -- Not so much a strategy as it is a kind of sub-game for LoL players, ARAM stands for All Random All Middle, and plays out exactly as you would expect. Random Champion picks for both teams that smash together in the mid lane until one team loses the game.
In Conclusion --
Finding strategies to beat the metagame is an entertaining exercise in itself, and while I take a fairly aggressive stance against tricky play, I do so only because when you are starting out, even once you hit 30, you open yourself up to crushing defeats as long as the other team is able to react fast enough to your chosen course of action. When I address each strat individually, I will expand on the counter play options that each is susceptible to, but for now, be confident that knowing your role and playing the traditional team is your easiest route to success and skillful play.
Until next time, may all your ultimates end in kills and all your games with "Victory."