Captured German equipment in Soviet use on the Eastern front

During World War II, losses of major items of equipment were substantial in many battles all throughout the war, with no exception on the Eastern Front. Due to the expense of producing such equipment as replacements, many armies made an effort to recover and re-use enemy equipment that fell into their hands, applicable to both Nazi Germany and the Soviet Union.
Equipment capture.
Small items of equipment such as personal firearms, clothing and uniforms and so forth are routinely lost as personnel are wounded, killed, or taken prisoner. There is often a perception amongst soldiers that foreign equipment is better or more convenient than the equipment issued by the soldier's own army. Thus, it was not uncommon for Soviet troops to make use of German boots, knives, mess-kits, flashlights and other personal items such as shavers and sidearms. Likewise, German troops often sought Soviet winter boots (vаlenki) and hats. Oddly, troops on both sides each favored the other's submachine guns. Photos of German troops using Soviet PPSh-41 submachine guns are as common as photos of Red Army troops (and Soviet partisans) using captured German MP-40s.
For larger items such as tanks, cannons or artillery pieces, equipment can be lost when they are immobilized through vehicle breakdowns or minor damages. In general, a retreating force tends to lose a lot of heavy equipment regardless of actual combat losses. The heavy maintenance demands of armored fighting vehicles are both a cause of loss and an obstacle to re-use. For example, after the Battle of Stalingrad in 1943, several hundred German Panzer III tanks and similar StuG III assault guns/tank destroyers were captured. So many were available that a significant effort was made to repair and re-use them. More than 100 were rebuilt as the SU-76i self-propelled gun, with some even serving as Soviet SG-122 self-propelled howitzer vehicle prototypes. Besides Panzer IIIs and StuG IIIs, the Soviets also used about a hundred ex-German Panzer IV medium tanks and (at least) some Panther tanks. Tiger I and II tanks seized by the Soviets were only largely used for testing rather than fighting on the frontline (no photographic evidence of any serving on the front). Artillery pieces can also be lost during retreats, when battery positions are overrun (often easily once the frontlines are punctured) or when they are immobilized during hindered road movements or maneuvers.
On the other side, Nazi Germany fielded a large quantity of their own captured enemy weapons ranging from rifles to tanks. In particular, the German military used hundreds of T-34/76 tanks which fell into their hands early on in the war, as did several hundred other older and lighter models such as the T-26 and a handful of KV-series heavy tanks. Captured Soviet rifles and submachine guns were also operated by German soldiers, as were artillery guns of various types, such as the 76mm anti-tank/field gun, that were lost by the Soviet Red Army as they rapidly retreated eastwards all throughout 1941.
Use of captured equipment.
Captured equipment was of more value to the Soviets as a source of intelligence on German equipment capabilities and weaknesses than they were for use on the battlefield. The first examples of German Tiger I tank and Königstiger tanks captured in combat were sent to Soviet proving grounds for evaluation. Photographic evidence does exist of usage of German equipment by the Soviets, but their use was usually for short periods of time.
Use of captured equipment has obvious benefits and less-obvious drawbacks. When Axis tanks were captured and could be repaired for use, they were often used in deception operations. A common tactic was for a Soviet tank unit to approach a German position using one or two captured German tanks in the lead. The hope was that the German defenders, recognizing a "friendly" tank, would not fire, or would delay their fire long enough for the Soviet unit to make a close approach.
Axis tanks and other AFVs were also re-marked and sometimes re-armed with Soviet weapons. One such example is the SU-76i assault gun based on captured Panzer III. Evidence also exists of German Panzer I-based command vehicles re-armed with Soviet 20mm ShVAK cannons. Usually, however, the vehicles were neither modified nor re-marked.
The drawbacks to using enemy equipment are significant. First, the captured vehicles are very often mistaken as enemy and thus are subject to friendly fire. Second, it is difficult to repair or maintain them; the simple act of obtaining ammunition or minor engine parts can be insurmountable. Third, equipment such as radios may not be compatible with other friendly equipment. Fourth, troops may not understand the maintenance requirements of the unfamiliar enemy equipment. 
With the exception of the Panzer III tank, most of the vehicles listed below were captured in very small numbers and never contributed significantly to Red Army strength in any operation.