What type of mines and booby traps did the germans use?
Mostly, German ones. 
Do you mean anti-personnel or anti-tank or naval mines?
Manufactured booby traps or field rigged ones?
Well… if you like German anti-personel mines as a proper start for the additional elaboration of this intriguing theme, I think that I do have something for you, my dear Mr. Glider Infantry – a color snapshot of a very fashionable German Stockmine 43.
Positioning of the Stockmine 43 by a German sapper
This fragmental antipersonnel mine was mounted on a stake, and triggered by trip-wire, and intended for incapacitation of enemy’s infantry.
Essentially, this 2,23 kg heavy land mine was wery simple: it consisted of a cylindrical concrete body with numerous steel fragments premixed into the row concrete mass. A standardized 112 g Bohrpatrone (TNT cartridge) was inserted into the body through the base, and a highly sensitive ZZ35 or ZZ42 igniters were screwed on (through the hole) onto the top of it.
The mine was fixed onto a wooden stake, which also held the previously mentioned explosive cartridge in place. The mine was set off by a tripwire. After arming of the igniter, a pull on the tripwire moved the plunger upward against the resistance of the compression spring. The two locking pins were forced outward when they came-up to the open spaces, thus releasing the striker. The released striker, driven by the striker spring, set off the percussion cap, and the job was done.
However, it has to be mentioned that this type of APM has been equipped with so called S-Minenzünder 44 (SMZ 44) as well, which operated by direct pressure. In that case the mine was dug in the ground, and only the detonator tip stack out of the ground. Efficiency of the Stockmine 43 in this case, however, was noticeably lower.
After the war Yugoslav Peoples Army adopted a very similar variant, that due to its robustness was in active use even in early nineties, during the sorrowful Yugoslavian civil war.
Don´t know what kind of booby trap, but the Germans did use them to booby trap dead bodies during their retreat into Norway in 1944/45.
I know from my grandpa how they occasionally killed tanks in an ambush on the eastern front. They attached 3 or 4 AT mines and a rope to a wooden board and hid them on the opposing side of a road. When the tank approached they pulled the board on the street so the tank would run over it, triggering the explosion of the mines.
Hello Drake.
A modified ‘Gestreckte Ladung’ with Tellermines - known since World War One and teached also 
[here with Handgrenades]
http://www.erster-weltkrieg.net/deutschland/heer/
Wheren’t there some beach obstacles also like that? ‘Board-Mine-Stick’? /o/i http://www.lonesentry.com/manuals/german-coastal-defenses/minefields.html
€: There was a great mine information site, a Dansk one, but i can’t find it anymore …
Stockmine43 http://de.wikipedia.org/wiki/Betonmine [wikipedia ^^]
Tellermine and under a little suprise: another one 
When you disarm the first,and hold up,the second is blow up