There are many organizations on both sides of this incredibly important issue in US politics. I hope to give short descriptions of a few of them. This will be a long diary, so the rest will be after the orange squiggly. In fact, I'll only do one side in this diary, I'll wait until some time later to do the other side.
The only reason why the National Rifle Association has the longest thing is that they're the most prominent, so I am able to say more about them than about any other organization because there's more information available.
1. The National Rifle Association
The National Rifle Association was founded by two US Army officers after the Civil War to promote marksmanship (directly contradicting Michael Moore's inference that they were founded by the other side), as they were appalled by the poor marksmanship displayed by US forces in the Civil War. They have, since 1871, promoted hunting and other shooting sports. In the past fifty years, they have also become political advocates. They have 4.3 million members who either pay an annual fee or bought a $1000 life membership, and membership fees make up 85% of their budget. As a pro-Second Amendment person of liberal views, I view them as a necessary evil. If not for them, the turn toward gun control starting in the 1970's would very likely have far more disastrous consequences than the Hughes Amendment, the 1994 law, and other bans on "assault weapons." However, the ILA, their political activism arm, is rather obnoxious and often supports Republicans when Democrats would actually be friendlier to their policy objectives, such as the 2009 Virginia gubernatorial election. Another thing that turns many people away from them is the fact that they tend to attract some over-the-top personalities. I can understand Ted Nugent behaving in that manner, as he's based his career around being an over-the-top performer. I can also understand R. Lee Ermey saying a few over-the-top things (but I can only think of one particularly strong thing he said and he had the decency to issue an apology for it), as he's a former Marine Corps Drill Instructor, a job known for such exclamations, and most of his acting career has been either a similar personality or, on occasion, the exact opposite personality as a joke (The NRA's recent "Trigger the Vote" ad featuring him as a librarian is one such example, and is hilarious due to the idea of him speaking in a soft voice). However, most of the high-ranking NRA figures, such as Wayne LaPierre, have no such excuse, coming from careers where over-the-top outbursts either don't matter or, more likely, are highly unusual and frowned upon. There's a lot to criticize about them, but the way that some people seem to view them as a supervillain responsible for the defeat of any restriction on firearm ownership is rather idiotic.
2. Gun Owners of America
These guys are insane. Birthers, militia insurrectionists, and their ilk have a home here. The only members of Congress who they consider acceptable on the issue are Ron and Rand Paul. This should raise a few red flags: there are many other members of Congress who have an equal voting record on Second Amendment issues to Ron Paul, and Rand Paul hasn't had a chance to display his actual positions. In fact, they've fought against some things that they should support. For example, they fan the flames of conspiracy theory against the recent bill in the House to enforce the Full Faith and Credit clause of the Constitution with regard to concealed carry. Why do they do this? They're a mouthpiece for the most radical interpretation of the Tenth Amendment. They care more about radically changing the Tenth Amendment than they do about defending the Second.
3. Second Amendment Foundation
I don't have much to say about these guys. They know the right way to do things, and they do that incredibly well. Instead of being at the forefront, they work from behind, through the courts. While the NRA's top priority is funding people who say obnoxious things with funding important court cases as a secondary priority, the SAF focuses almost entirely on important court cases. The lawsuit that ended the DC handgun ban was funded by both the NRA and the SAF. The next big lawsuit, which ended Chicago's similar law, was funded entirely by the SAF. They don't make prominent statements on current events, but they handle themselves incredibly well when they do make statements.
4. Jews for the Preservation of Firearm Ownership
I don't really know much about them, but I think I like them because I'm incredibly suspicious of law enforcement and think it needs to be scaled back greatly, as they call for the abolition of the Bureau of Alcohol, Tobacco, Firearms, and Explosives (in my opinion, federal law enforcement should only be the FBI, the US Marshals' Service, and the Secret Service). To my knowledge, they do not comment on current events at all. I would like to see more statements from them that don't invoke the Holocaust, as the frequency at which they reference the Holocaust is excessive regardless of the fact that the 1968 Gun Control Act was patterned after a law that Germany enacted thirty years previously. However, they definitely do a good job showing the connection between gun control and Jim Crow.
5. National Shooting Sports Federation
This is the industry's lobbying group. As far as I'm aware, they only exist to host the Shooting, Hunting, and Outdoor Trade Show every year and as evidence against the claims that the NRA is controlled by the industry. As representatives of US firearm manufacturers, they have acted against the interests of their customers, such as supporting import bans and other such things. One thing that they have done is attempt to create an alternative to the BS term "assault weapon." However, even though the most popular target shooting disciplines require such rifles and they're the most popular rifles for hunting coyote, mountain lion, and other predators, the term "modern sporting rifle" will never catch on. The good thing about it is that it's not designed to deceive, as "assault weapon" was. However, most people who use such rifles call them "tactical rifles" or something like that.