You can play any way you want to and do not have to jungle. However, some champs are so good at jungling, that one usually prefers that to normal laning (Amumu, Shaco, Skarner and the like).
You are right, that a jungler means that one other player is left alone against two enemies. However, he has the protection of a turret, which is enough in the early game to survive. Plus, he levels almost twice as fast as his two enemies, so he will very soon have his ultimate available against two level 3 or 4 enemies. Of course, some champions have a hard time to stay alone in a side-lane. Make sure when you have a jungler in your team, that you have a solo-champ that can hold its own without problems.
Jungling can only theoretically be done by all champions (sure, anyone can go into the jungle and attack creeps there). However, most champions are way too slow to make it worthwhile. They would profit much more from staying in a lane. These champions should not try jungling. If you want to try jungling yourself, then select a champion, for which you have one of these jungling guides at hand. Don't just try any random champion out in the jungle.
Finally, the most important point about jungling is one that most novice players often forget. You do not jungle in order to remain in peace and level up on your own. You jungle, so you can level up and at the right moment appear in a lane for a surprise gank. Enemies have to be constantly aware that a jungler may pop out of a nearby brush all of a sudden turning their 1v1 or 2v2 lane into a 2v1 or 3v2 problem. If done right, jungling can very quickly devastate your enemies, because the jungler has the power to turn around any lane. If one of your team's lanes is having trouble, adding another champion to it will devastate the enemies and at least break their attacks. Often, you can even net a kill or two. If you're a good jungler and help out frequently with ganks, then you will soon outlevel your enemies and the game can be pretty much decided in less than 20min.
So in summary, do not doubt jungling. It is a very popular and strong strategy. However, be aware that being a good jungler is not easy. Especially, when playing together with other novices, who may not know how to deal with a jungler in their own team. I suggest, you try to get at least several dozen games of normal lane-gameplay done, before you try out jungling yourself. And then, start with practice games, so you are certain, that you will survive the early jungle farming. It is most embarassing to die to the golem when no enemy was ever present.
Let me stop you in your tracks mate :)! The thing about eve is that she is squishy and is played poorly very often and is easy to mess up. People misunderstand her for good reasons because she rarely shines and ends up feeding.
I have had success with her jungling by how she comes out of stealth and has the slow along with her e which shreds armor. Her ult allows her to gain health after a kill and move super fast. That is a perfect jungler description: a champ who can gank well and have some way to slow to have the laning champion(s) catch up.
I have had some success laning by being aggressive early (know your limits however) and then farming up while they stay back, some teams have eve roaming nonstop and a jungler on the side, while having only 1 champ in each lane.
It is true though she isn't really played in tournaments, but I have seen her in the high elos (2000 range) and those players know how to play her well!
Best Answer
Yes, it's worth it to pick another jungler. It does not necessarily have to be a counter-pick though, which probably needs some explanation:
Anyways, double jungle teams are quite a common thing, because neither team wants to ignore the advantages gained by having a jungler. However, it also means that your team should know how to deal with that situation. Here's a few tips for general two-junglers-play:
As you can see, two junglers are possible, do make sense, and generally lead to very fast and intensive gameplay. Beware on random groups though, as a two-jungler game demands a lot more from all players and failure is easy to achieve in that setting.