I listed some of the glitches that really bug me.

1) Half slab glitch: Make a tower of half slabs going from top to bottom (at least 2 blocks high), and then put a similar slab on top. They will all combine into a double slab making you lose whatever extras you put.
2) In SMP, lure a creeper to a corner and get out of sighting range of it. Have one of your friends take a look. It will be friendly to him, that is, until you yourself disconnect.
3) In SSP, Make a double door layout like so:
D D
P Re
R R
where R=redstone dust, Re=redstone repeater, P=pressure plate, and D=door
you will notice that passing through the automated door at a certain angle will make you phase through the block directly under you.(much like minecarts in 1.5 going back, when you tried to mine it while riding it.)
4) Make a jointed chest (a large chest with a small chest adjacent to it) in version 1.5 of minecraft and play the world in version 1.8 onward. You will probably be like "...WTF..." when you see animation of opening it.
5) Drop an item (any item) and save your game. Load the world again and pick up the item. Press escape but don't save and exit. Instead, close the window and reload minecraft. When you come back to your save game, you will have double of whatever you dropped.
6) put a redstone power source of any location. Then put a piston on the block diagonal to it and with a lever next to it. Set this up with ice touching the piston arm. It should look like this:
P L ===>> P L
I Rt P Rt
I
where P=piston, I=ice, Rt=redstone torch, and L=lever
when you power the first piston, the ice should be pushed. retract the arm and put another piston facing the same direction. The Piston head will magically disappear.

I plan to add more. This is my first post so go ahead and post any comment. I am interested at what you guys have to say. :D