In today's age, when dogfights are simply a relic from the past, why do manufacturers keep on increasing their aircraft maneuverability, in order to make them better dogfighters. It is more understandable if they were to make stealthier or more efficient fighters, but when the dogfight is extinct, why make planes even more agile and maneuverable?
That same thinking, "dogfighting is dead", got the USAF and USN in serious trouble in Vietnam. The U.S. Armed Forces were convinced that the next major war would be against the Soviet Union directly, in theaters including Europe, Alaska and Canada, and as a result, fighter designs succeeding the very successful Sabre and Super Sabre day fighters used in Korea began emphasizing standoff capabilities, believing the aerial threat would come from various classes of nuclear bomber, calling for fast, long-range missile-armed interceptors as a counter.
That war, thankfully, never materialized. Instead, the U.S. was pulled into more or less another Korea, a proxy war fought between Soviet-supplied and trained Communist forces against a U.S.-backed fledgling democracy. The big, heavy U.S. F-4 Phantom interceptor and F-105 Thunderchief light bomber, neither of which had internal guns, found themselves facing the older like-minded successor to the MiG-15s they faced in Korea, the MiG-17, coupled with the MiG-21 close-range interceptor. Instead of the long-range standoff air war the USAF was built for, US pilots were ambushed at close range by guns and infrared missiles, resulting in a piss-poor 2:1 kill/death ratio in aerial engagements, compared to the 14:1 ratio they enjoyed in Korea.
The result was increased attention paid to "air combat maneuvering", and an emphasis on this style of combat in the next generation of fighters adopted by the U.S. military. The F-14 and F-15, though intended to bring back dogfighting (and they did), turned out to be big, fast interceptor-style fighters like their predecessors, that still only had a clear advantage in BVR engagements. So a group of USAF generals, seeing what its allies had been doing with the F-5 Tiger that the Joint Chiefs had more or less passed on (a few trainers, a few aggressor planes, but no combat adoption), commissioned the LWF competition, which would produce the F-16 and F-18 lightweight multirole fighters with an emphasis on the close-quarters maneuverability that the Communist powers never really forgot.
The F-22 splits the difference between the F-15 and F-16's air combat strategies, producing a heavier but highly maneuverable fighter that excels at air combat at any range (but is so expensive that so far the USAF have only deployed them in situations where they would never face any real threat). The F-35, however, is rapidly becoming a disappointment; compared even to the F-16 or F-15E it will replace, it "can't climb, can't turn, and can't run", and the A variant is the only one with an internal cannon (which carries only 182 rounds of ammunition compared to the F-22s 480, the F-15's 650 and the F-16's 510); the STOVL B variant and the Navy's C variant won't have guns at all.
In today's military theater, the U.S. enjoys "air supremacy"; we're fighting largely paramilitary forces with practically zero air to air capability. Tomorrow's theater, however, may be quite different. Diplomatic relationships with a number of Russian-supplied nations including Russia itself are souring day by day, and the U.S. could easily find itself drawn into conflicts over Taiwan, the Korean peninsula, India/Pakistan, the Ukraine, etc, where they'd face militaries fielding Russian jets purpose-built to mix it up at visual range.
In short, while the U.S. hasn't directly fought a conflict against a serious air threat since Vietnam, there are a lot of potential near-future conflicts in which they would get their chance, facing the Sukhoi PAK-FA or Chengdu J-20 with skilled Chinese or Russian pilots at the stick. Even if these fighters aren't fielded in mass numbers, the U.S. would still face the Russians' direct answers to U.S 4th and 4.5-generation fighters, including the MiG-29 and Su-27/30/33. Many variants of these were specifically designed to out-maneuver the U.S. F-15, F-16 and F-18 (which would likely be the first jets in-theater), and which would still be a match for the F-22 in a visual-range "furball".
Dogfighting isn't dead. Even though generation 4.5/5 airframes have great missile capability and stealth, there are times when there is no substitute for bullets. Close quarter gun fire is pretty much immune to chaff and flares. Being able to maneuver into position to engage another aircraft with guns is essential in many circumstances and training for that will likely be a fundamental part of flight training for a long time, so, I doubt that manufacturers will stop developing more maneuverable jets even though electronic/computer systems are playing a larger part in air to air combat.
Some good answers here, in complement to which I would like to submit a very interesting paper (alternate link - pdf!) I came across on the promise vs. reality of BVR combat, which has been predicted to replace dogfighting since the 50s, if not 40s.
In short, history has shown that despite all advances, battlefield realities have consistently forced aircraft into close-range situations where traditional ACM capability still matters, so manufacturers have to take that into account if they hope to sell their aircraft. The only reason dogfighting is extinct in Afghanistan is because insurgents there have no aircraft of their own to operate. Operations elsewhere have demonstrated the continued relevance of having a platform that can maneuver when it has to.
There is, however, a reverse side to the coin in that, while maneuverability and thrust-to-weight ratios remain important, we may be hitting a plateau in terms of how much more that capability is being improved. So-called "supermaneuverability" is becoming a fairly ubiquitous feature in most modern dedicated air superiority fighters (e.g. F-22, T-50, Super Flanker series, the Eurofighter Typhoon in its air superiority configuration, etc.) but the levels of agility currently on display have often been first showcased more than 20 years ago.
In the meantime, other features such as stealth, supercruise, passive and low-probability-of-intercept sensor suites, data links, helmet-mounted sights and off-boresight launch capability for missiles, along with a massive push towards improving pilots' situational awareness have seen tremendous advances in the past 20 years and, to my mind, say a good deal about what the air forces of the world (i.e. the customers) perceive to be the elements that will give them an edge.
In short, dogfighting capability is still regarded as an essential capability, but only time will tell if its importance will diminish relative to other elements.
The manufacturers aren't trying to increase their aircrafts maneuverability. The F-35 is far less maneuverable than the fighters it is replacing. Modern selling points include stealth, multi-role, reconfigurability, avionics, price, and data. It is all about Situational Awareness.
General Hostage of USAF says:
People focus on stealth as the determining factor or delineator of the fifth generation. It isn’t; it’s fusion. Fusion is what makes that platform so fundamentally different than anything else.
Lieutenant Colonel Berke says:
But the difference between a Hornet or a Viper and the Raptor isn’t just the way you turn or which way you move the jet or what is the best 43 way to attack a particular problem.
The difference is in how you think. You work in a totally different way to garner situational awareness and make decisions; it’s all different in the F-22. With the F-22, as will be the case with the F-35, you’re operating at a level where you perform several functions of classic air battle management. That’s a whole different experience that requires a different kind of training.
And from another pilot:
The whole point to fifth generation is the synergy of stealth, fusion and complete situational awareness," says a veteran Air Force fighter pilot. The point about fifth generation aircraft is that they can do their mission anywhere - even in sophisticated integrated air defense [IADS] environments. If you fly into heavy IADS with a great radar and sensor fusion, but no stealth, you will have complete situational awareness of the guy that kills you.
Maneuverability and dogfighting isn't a selling point. In fact lt.col Berke specifically dismisses it.
Moreover, the answer from KeithS seems quite off. The F-105 Thunderchief was a ground attack fighter-bomber.
As a follow-on to the Mach 1 capable North American F-100 Super Sabre, the F-105 was also armed with missiles and a cannon; however, its design was tailored to high-speed low-altitude penetration carrying a single nuclear weapon internally. [...] During the war, the single-seat F-105D was the primary aircraft delivering the heavy bomb loads against the various military targets. Meanwhile, the two-seat F-105F and F-105G Wild Weasel variants became the first dedicated Suppression of Enemy Air Defenses (SEAD) platforms, fighting against the Soviet-built S-75 Dvina (NATO reporting name: SA-2 Guideline) surface-to-air missiles.
Of course it isn't going to be a great dogfighter. Still, it rackered up nearly 30 MiG kills. The F-4 however was an Interceptor with standoff weaponry,
[its] biggest weakness, as it was initially designed, was its lack of an internal cannon. For a brief period, doctrine held that turning combat would be impossible at supersonic speeds and little effort was made to teach pilots air combat maneuvering. In reality, engagements quickly became subsonic, as pilots would slow down in an effort to get behind their adversaries. Furthermore, the relatively new heat-seeking and radar-guided missiles at the time were frequently reported as unreliable and pilots had to use multiple shots (also known as ripple-firing), just to hit one enemy fighter. To compound the problem, rules of engagement in Vietnam precluded long-range missile attacks in most instances, as visual identification was normally required. Many pilots found themselves on the tail of an enemy aircraft but too close to fire short-range Falcons or Sidewinders.
So while it wasn't designed as a dogfighter, that isn't the cause of its low kill:death ratio. Politics and 60s-70s era technology was.
Haven't you seen Independence Day?
It's always better to be prepared for a category of threat than to write it off. Why teach a soldier hand-to-hand fighting when he has an assault rifle? Because you don't want to lose a perfectly good soldier when he gets surprise-jumped and doesn't have the time or space to bring his rifle to bear.
Additionally, the recent Defense spending trend in the U.S. is very large, very expensive orders of a particular vehicle. Those numbers are much easier to sell when that vehicle can (on paper) fulfill multiple roles. Just like in business, you're going to have some marketing wizard who's only job is to secure the biggest budget possible for your pet project, and his goal is to have an endless bullet-list of features to attract those dollars.
From what I have read, and from the answers I have seen above, it looks like most of air combat will consist of BVR missile attacks, however, since nothing is 100% perfect, some of fighters will get through the initial missile salvo and end up in close - range air combat.
Why do manufacturers focus on "making their planes more dogfight-worthy?"
Answer: Just in case
This document may be useful: