What kind of weapons that were popularly captured in WWII?

The most desirable souvenir was off of German soldiers was a Luger, practically the best pistol during that time. Often times only officers carried these, so it was also a prestige thing. For Japanese soldiers, it was most definitely the katana or the Japanese samurai sword. Only high ranking officers had these too. The bayonets of the Japanese army was also unique since it was extremely long. The Type 99 rifle is also a cool Japanese rifle to have, a friend of mine still has one as a WWII souvenir.

As for what they took off of American's, I have no idea.

Allied soldiers liked the MP40 type weapons, lighter and more reliable than their own automatic weapons, plus took normal 9mm rounds (they couldn't use the MP-44 because no ammo) German pistols were popular for a number of reasons, firstly most soldiers didn't have pistols and soldiers always like having a little insurance in case their main gun breaks, so getting a pistol was always a no1 priority for combat infantrymen, secondly the luger was an iconic gun even before WW2 and troops liked getting them as they could be sold later. The MG42 was always popular but no allied ammo worked in it.

everyone liked the Japanese officers katana swords (samurai swords) - pretty obvious why!

The germans liked the Russian ppsh sub-machine gun, same 9mm ammo as the MP40, but with 72+ rounds per clip vs 32 rounds in an MP40, it was very tough and reliable and very, very popular with the german troops, as mentioned above Russian pistols were also popular (for the same reasons German pistols were popular with allied infantry)

(all soldiers in every army wanted pistols - since their own army didn't give them out, they had to take captured ones instead)

hmmm i think there wasn't any real taking of weapons more like stealing helmets, gold teeth, lighters, weapons not so much since they didnt have ammo for the weapon so it was only usefull for a small amount of time. Allies did lie to take the Panzer a lot lol my grandfather drove a Panzer in WWII. "those damn people took my tank"-in cute old greman man voice lol but they destroyed them and used them for their scrap.