I guess I'm going to deviate a bit from the consensus with my response. At first, I was going to go with something along the lines of the Q3 railgun (or any other hit-scan weapon, such as the shock rifle) but it occurs to me that these weapons tend to be exceptionally powerful (shot per shot the railgun was the deadliest weapon in Q3) and the difficulty in their use varies with range. At long range, it's trivial to get a hit with a railgun, but at point blank range, accuracy is essential as you probably won't get a second shot.
Melee weapons, by definition of function as a weapon of last resort hardly qualify. Only a fool (or someone who makes a habit of playing against sacks of lettuce) would choose to use one as a primary weapon because the odds of winning in the long term are so laughably low to make it an absurd choice for primary weapon. Even in Call of Duty, where the melee attack is an instant kill you find that most melee attacks are conducted because one is out of ammunition or attacking a target unaware.
Assualt rifles, as a general rule tend to be the weapon of ultimate utility and therefore tend to be fairly easy to use with some success. As such, the battle rifle from Halo is out, as is the primary armament in most FPS games.
Shotguns, and similar weapons (such as the flak cannon) are more difficult to use because of their limited range and therefore require a fair amount of skill in maneuver along with decent map knowledge and excellent aim to use effecitvely. Like the railgun, you often don't get many follow up shots with the shotgun style weapons, but the weapon does tend to be exceptionally powerful (Generally, if only one weapon is capable of a one-shot kill, it's as shotgun).
It seems that my own choice will likely be contriversial for the younger generation of gamers, especially people who ever played games like Quake 3: The Rocket Launcher. It should be noted that I am speaking specifically about the Quake 3 rocket launcher specifically becase of how the game was balanced. The rocket launcher, as one might suspect did a fair amount of damage on a direct hit, but even so it took a full three shots on average to kill a freshly spawned player. The weapon also had a moderate area of effect meaning that one could generally at least deliver SOME damage to their opponent. But, it was because this weapon was present on every single map (or at least every map I ever played) and even served as the focus of one of the most popular mods (Rocket Arena (and, yes, I'm aware of Instagib)) that it gets my vote. Travel time meant that only the elite players could consistantly land direct hits on a moving target, and often matched involved coralling an opponent with maneuver and rocket fire in order to deliver the klling blow. But the rocket launcher was more than just a weapon of war - it was also a means of locomotion and rocket jumping proved just as important as circle strafing and bunny-hopping in the long term. While much of one's success in Q3 came in knowing when to use a particular weapon (and where to get the best items), mastery of the rocket launcher was probably the single most important skill for one to learn. Being a crack shot with a railgun or a killing machine with a lightning gun only granted an edge on a handful of maps in a handful of circumstances - excelling with the rocket launcher was an assset on any map in virtually any situation.