Such an open ended question...

What caliber and ammo type (handload, factory or match?

Semi-Auto, Revolver or single shot (single shot could be breech, bolt, etc...)?

Who is shooting it (accuracy depends on the shooter, not so much the gun)?

Is it free standing or bench (bench in hand or bench in vise)?

Scope or Iron sights?

Barrel Length?

I would tend to go with a single shot, 8" plus barrel, scoped handgun in a bench vise, shoot indoors at room temp being the more accurate

For semi-autos, the Sig 210 has long been reputed to be one of the most accurate ever :

http://en.wikipedia.org/wiki/SIG_P210

The single most accurate pistol I've ever owned (I've had dozens of handguns in my 55+ years, including four-figure target pistols) is a Bersa Ultra Compact 9mm. I'm STILL surprised at how accurate it is. I can shoot 5 round strings with it into a 1" or less circle, offhand, at 30 feet all day long. I've had it almost 3 years and wouldn't trade it for any pistol I've seen either before or since I bought it, regardless of price. Actually, I've been so impressed by it, I decided to buy a second one last month.

Originally Posted by DRAEGER

Who is shooting it (accuracy depends on the shooter, not so much the gun)?

The shooter has nothing to do with the accuracy of the gun itself, as a mechanical object. All guns have a certain mechanical level of accuracy that is totally independent of the shooter. There is a difference between a gun's mechanical accuracy and its practical accuracy. Sights, trigger, grip configuration, etc. all play a part in practical accuracy, but have nothing at all to do with mechanical accuracy.

Scope or Iron sights?

Practical accuracy again. Mechanical accuracy has nothing to do with sights.

Barrel Length?

Barrel length, especially as it pertains to sight radius, has far more to do with practical accuracy than mechanical. In rifles, for example, short barrels are often seen on benchrest and sniper rifles. The short barrels are stiffer, and this stiffness is thought to make them more accurate (mechanically). Many 2" revolvers will shoot just as well as their 6" cousins from a machine rest, taking shooter error out of the equation.

To illustrate the difference between mechanical accuracy and practical accuracy, let's say I have two 1911s. One has been mechanically tuned and fitted with a match barrel by a top 'smith, but he hasn't improved the trigger and the sights are the vestigial A1 versions. The same smith has taken another 1911 and tuned the trigger to a nice 3.5 pound break and installed Bo-Mar sights, but left the barrel and such as-is. Which will I shoot more accurately? Most likely the latter gun, even though it is technically less accurate than the former, because its "human interface" is much better.

I would tend to go with a single shot, 8" plus barrel, scoped handgun in a bench vise, shoot indoors at room temp being the more accurate

Theoretically, if you are shooting from a vise, the scope is pointless, since the vise eliminates sighting errors.

I have an old Smith & Wesson model 64 .38 special that will put 148 grain wadcutter holes anywhere you want to put them

My HK USP Compact .40 is scary dead on. I just thought my M&P .40 was accurate.