They did use a few, actually; the M26 Pershing entered late in the war, and the Army was experimenting with other heavy and super-heavy designs when the war ended. However, the US didn't use many heavy tanks for a few reasons.
US tank doctrine in WWII emphasized that American tanks should avoid fighting enemy tanks. Killing enemy tanks would be left to anti-tank units, equipped with AT guns and purpose-built tank destroyers. The M4 Sherman was to be used to support the infantry and to break holes in the enemy line and use their superior speed and maneuverability to outflank the enemy, cut off his supply lines, and hit vulnerable targets like artillery and supply dumps.
There were logistical concerns. Later on in the war, the US realized that Shermans were horribly outgunned against German tanks, but by having fewer types of tank, you simplify logistical problems. You need fewer types of spare parts, fewer varieties of ammo, etc. Also, heavy tanks cost more to ship. The M26 weighed 50% more than the M4 and took up more space, meaning that fewer could be shipped at once. This leads into the third reason.
The US valued having more tanks over better ones. 49,234 Shermans were built, compared to a total of 16,392 Tiger Is, Tiger IIs, Panthers, and Panzer IVs. Also, half of that number is Panzer Ivs, which Shermans could handle, and keep in mind that by D-Day, many of those German tanks had been destroyed in North Africa and on the Eastern Front. So in France and Germany, the US had 3-4x as many tanks as the Germans. German tanks were more heavily armed and armored, but this didn't matter. Tanks vs. tank battles are and were rare. The truly important thing is having any tank at all to take ground and support infantry, and having more tanks allowed the Americans to provide more units with tank support. Furthermore, German tanks were mechanically complex, very heavy, and short on spare parts, so they broke down all the time. On the other hand, American tanks were extremely reliable and easier to fix. Lastly, in the event of a tank vs. tank battle, numbers are critical. Sure, a German Tiger was very powerful, but if you have 5 Shermans attacking it, they can hit the Tiger on its rear and side armor at close range. One Sherman can distract the Tiger while the others go around behind it. And in the worst-case scenario, you can just ignore the Tiger and drive off all of its supporting units, forcing it to fall back or else be destroyed by infantry with satchel charges. Or they could call in close air support to bomb the tank.
EDIT: Please note that I'm in no way asserting that the Sherman was better than the Panther/Tiger/Panzer IV, etc., I'm simply trying to explain why the US used the Sherman and what benefits they gained by not using a heavier tank. jonewer's post makes some very good points, and if you want to argue about which tank was better, you need to keep all of those factors in mind. I entirely agree with his post.
Again, with Sherman v. German threads, the basic fact is being lost that the primary function of the tank in WWII was not to face off against other tanks and that binary comparisons of this tank's gun against that tank's armour are essentially pointless.
So I will partly reproduce another post I made a while back below:
Tanks are not like fighter aircraft whose sole or main purpose is to destroy other aircraft and binary comparisons of one tank's armour, for example, against another is a very superficial analysis.
Tanks are a part of the combined arms weapons system. Real life is not World of Tanks. There is infantry, aircraft, barbed wire, inclines, infantry, artillery, mine fields, infantry, anti-tank ditches, logistics, infantry, production costs, ease and speed of construction, infantry, reliability, maintainability, infantry and infantry.
Did I mention infantry? Because that's what matters in war. Only infantry can occupy and hold ground and the primary function of all other facets of combined arms warfare is to allow the infantry to occupy and hold ground.
The efficacy of any tank must therefore be measured in a holistic manner, and not in a reductionist stats analysis. For example, is the velocity of the main armament the principle determinant of how good a tanks is? Is armour penetration even the principle determinant of how good a tanks is? And the answer is obviously "No".
If this was the case then the 2pdr and 6pdr guns on early to mid war British tanks would have imbued them with a firm superiority. In fact, these guns were totally unsuitable as tank guns because they could not fire a meaningful HE round and were thus ineffective against infantry, artillery, and just about anything else on the battlefield that wasn't a tank.
Not only that, but these uber high velocity improbably long boom-sticks that the Germans mounted on their late war tanks were a liability in close terrain (hedges, forests, urban areas), while the muzzle blast kicked up dust, stripped leaves from bushes and trees, and were a menace to any supporting infantry who might be in the vicinity.
So a very high velocity gun is useful for shooting up armour, but its less useful for everything else. And how important is shooting up other tanks? Well, analysis conducted by the western allies indicates that only around 14% of all tank casualties were caused by other tanks which is about the same as losses to panzerfausts.
Which simply reinforces the point that primary purpose of a tank is otherwise than killing other tanks. Again, this was a central pillar of pre-war British armoured doctrine and it was proved horribly misguided.
So in evaluating how good a certain tank was against another we need to evaluate everything. Including speed and cost of production, ease of supply, ease of maintenance, reliability, transportability, and value as an infantry support tool.
And in all of those factors, the Panther and the Tiger fall flat on their faces. Hell's teeth, would you buy a new car if the manufacturer estimated it would suffer a catastrophic transmission failure before your first visit to the petrol station? Or a car that had to be fitted with an automatic fire extinguisher in the engine bay because of the frequency of engine fires? Of course you wouldn't, yet this was the kind of design feature built into the Panther.
So while the Panther and Tiger seem good on paper in the world-of-tanks reductionist-stats-analysis kind of way, actual events showed that the rather more humble allied tanks like the T-34, Churchill and M4, were a better weapons system overall.
All of the comments I've read here seem to be focused on the tactical doctrine of smaller tanks. I'd like so see someone with some solid knowledge comment on what I have heard.
It's my understanding that the main reason we used smaller lighter tanks than the Germans or Russians, was due to our auto industry.
We repurposed the machinery and assembly lines designed to make cars and pickups into making tanks, but those assembly lines were too small to accommodate the manufacture of full size tanks. So we made smaller tanks, lots and lots of smaller tanks.