To expand on Hussar's excellent reply:
Why can't they? An unarmed naked fighter still has all his feats while the naked casters may not even have spells left. These obnoxious scenarios don't prove anything. We can have butt naked fighters and monks but the butt naked casters have all their spells ready and intact. Do you see how certain situations get dressed up to try and support an argument? Melee people suck because they accept buffs from spellcasters and melee people always seem to be put in these hypothetical situations where people try and make them out to be horrible classes that can't do anything.
They can't do their main job because they rely on items and buffs to perform their primary functions. Example spoilered for space.
[sblock]Take an ancient black dragon, for instance, a fairly standard CR 19 threat right out of the book. A fighter can't get an AC high enough to avoid being hit by the dragon's +31 attack bonus solely from his own abilities, since even if he crafts his own armor he's likely getting at most AC 23 (10 + 3 Dex + 8 mithral full plate + 2 shield). A fighter can't get an attack bonus high enough to reliably (≥50%) hit the dragon's 38 AC solely from his own abilities, since even if he crafts his own weapons he's likely getting at most +24 attack (+19 BAB + 4 Str/Dex + 1 masterwork), and when he does hit it he has to put up with DR 15 without being able to deal all that much damage. A DC 31 Ref save against the breath weapon is out of his league (base Ref +6, plus max +4 Dex) as is the DC 28 Will save against Frightful Presence, and without Con boosters he has at max 266 HP, so he can't take more than a few rounds of full attacks from the dragon (bite/claw/claw/wing/wing for 4d8+6d6+33, average 72 damage or at most 4 rounds survived) and the dragon can strafe him with its breath for an easy victory.
At the same level, a wizard using only his own spells and feats can get an AC of 24 (10 + 6 Dex + 4 armor + 4 shield) plus several miss chances, and has a save DC of up to 29 (10 + 9 spell level + 8 Int + 2 feat(s)), which means a dragon will fail a save against his spell more often than it will be hit by the fighter's attacks. His saves against the dragon's breath weapon and Frightful Presence have a better chance than the fighter's (base Ref +6 + 6 Dex), his effective hit points are better (max of 190 HP, dragon's full-round does average 22 after DR 10, taking ~9 rounds to kill him), and the wizard can attack at range to make strafing less viable.
Feats can boost the fighter's numbers by 1-5, and boosting stats can add another 2 (though note that the above numbers assume 18s across the board for both parties, an advantage for the fighter), but every feat spent on boosting numbers is one fewer feat spent on getting more options, making a fighter a less-than-effective one-trick pony, and every stat boost spent on offense does nothing for defense and vice versa. Meanwhile, those buffs for the wizard are only the kind of stuff he'd have up all day or for multiple minutes at a time; if he casts a buff or two as combat starts, he can easily add +5 or more to relevant numbers (e.g.
nightstalker's transformation for +5 AC, +5 Ref, and evasion), start flying, prevent the dragon from flying, become immune to fear and/or acid, add miss chances, hide from the dragon, and much more.
Sure, it's
possible for a wizard to not have appropriate spells for the situation, even though by that level his buffs last all day and he has over 42 non-cantrip spells per day. But an itemless, unbuffed monk or fighter
can't ever handle that threat on even footing, and that example dragon didn't even have skills, feats, or spells picked that would make the challenge harder.[/sblock]
Now, once again: can
individual fighter types handle things, based on optimization levels? Yes; I'm currently running a martial character who walks around with an attack bonus of +46ish, average saves of +37, high damage, and high movement speed at level 11 without any items or buff spells thanks to very high stats and several add-X-stat-to-Y-bonus features, and there are charger builds that can potentially one-shot the above dragon without their items and buffs. Will this ever come up in
most games? No; you should have enough items to do your job just fine in most games, and enough party casters to buff you if necessary. Are martial types the
only item-dependent class? No, but casters only "need" a key-stat booster and can get by without one if they have to and spend their money on other things, while martial types need weapons, backup weapons, armor and other AC boosters, save boosters, and more.
Is this a
good thing? No; I remember the AD&D days when a 10th-level fighter could solo 3 trolls every 2 rounds without any magic items whatsoever and with minimum damage to himself, compared to a 3e 10th-level fighter who can solo 3 trolls every 4 rounds with a high probability of dying in the attempt (my favorite example, since the fighter and troll have the closest numbers between editions at that level), and I'm looking forward to seeing the 5e fighter
actually be the combat expert he's supposed to be. But as it stands, yes, the martial classes' base chassis could stand some substantial improvements.
Neonchameleon isn't right about his opinion on the matter because myself and a lot of other people don't agree. His view is highly subjective and arguable to the point of a stalemate. No class out there can do it all, there is no class that handle every situation that arises, sometimes a situation will come up that you need help from your other players because, in case some people have forgotten, that it's a team game. 4th edition didn't bring anything new to the table when it comes to teamwork, it only made the game where you essentially don't have a choice.
Now my views on 4th edition are subjective and open to arguments but at least I am man enough to own up to it. I don't keep spouting off about how my subjective views are right while everyone else's is wrong. But what I am right about is the fact that I don't like 4th edition now matter how much someone is telling me I am playing the game wrong. I have played 4th edition since it came out along with 27 years of gaming experience so I know if I like a game or I don't.
I'm not sure where 4e comes into things; I was only talking 3e, since that's the edition the initial scenario dealt with. And again, I never said anything about handling every situation or refusing buffs when they're available or anything like that. I only pointed out that there's a difference between "fighters are wimps, they can't possibly beat a cleric at anything" (which, as several people pointed out, is patently false) and "fighters cannot generally compete with level-appropriate challenges without relying on items and/or buffs" (which, as is shown with the above dragon example, is true).