Can Mice Climb Up Walls?

I am sure they must be able to climb up a certain amount of wall space.  I had a mouse (I guess it was really a shrew (sp?) which is basically a small mouse) come in my house through the back of a built-in shelf unit.  The unit was warped leaving the middle of it away from the wall, so the mouse must have climbed up the wall far enough to accomplish that feat, but it was probably easier between the wall and the back of the shelves.

Also, they sure can climb up cupboards - also a vertical surface.  I have had mice on my counter tops, and the only way they could have got there was climbing up the cupboard doors.  They even made it over the counter top overhang.