Naturally quite a bit of material fell into Allied hands in the ETO; especially after August 1944, when Germans tried to break out of the Roncey and Coutances pockets, and attempted to run the gauntlet forming around Chambois in the Falaise Gap. Most vehicles were destroyed by artillery, air and close assault; but many Panzer IVs and Panthers were abandoned - the trend would continue as ETO forces rolled towards the Dutch and German borders.
Both sides, as a standard rule of thumb, and if time was not immediately pressing, did their best to deny abandoned vehicles to the enemy. The ideal was to use explosives to completely deny the vehicle to the enemy; catastrophically destroying it. More often, disabling its combat capabilities by removing breeches, destroying optics or causing a split barrel with lighter ordnance was the best retreating crews and men could hope to do.
Now, unlike the Germans; captured tanks were not pressed into combat service in any truly noteworthy quantities- firstly as there was never a true dearth or lack of replacements. For the British their lend-lease M4A2s ran on diesel, whereas the Germans (like the Americans) ran on Gasoline; this already provided yet another reason not to use captured Panzers in combat - the added logistical strain of mis-matched fuel for the Commonwealth forces. Captured tanks were more often used in much the same way as captured aircraft; they would be shipped back to a quiet area, and put through their paces by Intelligence and Ordinance officials to rate and compare their capabilities. With tanks, we also have penetration tests; and often the most cited is the Isigny penetration tests. Unfortunately, penetration tests across all sides and nations often had to make due with battle-damaged captured models, and results were usually not always reliable compared to combat circumstances. Or worse, where flagrantly over optimistic at what shots could be made in combat situations.
One last note: In certain US Army units; operating with the 3rd Army and the 7th Army, the trend of stripping down damaged or abandoned enemy tanks to form 'Hillbilly Armor' was somewhat common. These additional steel plates would usually be rigged against the weakest or most vulnerable points of a M4A3; such as where its wet-storage ammo was, to reduce the effect of enemy penetration. Despite playing havoc with the tanks weight and balance, and strong objections from the commanding officers of both armies, the habit stuck.
Edit: Of note; the 501. and 503. Regiment d'Chars of the Free French were the only Western Allied force to make extensive use of captured Panthers both during and post-war. Their evaluations and exercises post-war with the mass of captured Panthers are of particular interest to tank tacticians, as the statement 'The Panther is not a strategic tank' is often first attributed to the French reviews of the vehicles.