How can a piece of A4 paper be folded in exactly three equal parts? This is something that always annoys me when putting an A4 letter in a oblong envelope: one has to estimate where to put the creases when folding the letter. I normally start from the bottom and on eye estimate where to fold. Then I turn the letter over and fold bottom to top. Most of the time ending up with three different areas. There must be a way to do this exactly, without using any tools (ruler, etc.).
Fold twice to obtain quarter markings at the paper bottom.
Fold along the line through the top corner and the third of these marks.
The vertical lines through the first two marks intersect this inclined line at thirds, which allows the final foldings.

(Photo by Ross Millikan below - if the image helped you, you can up-vote his too...)
This is a slight variation of the method of Egor Skriptunoff that works for paper of any aspect ratio, not just A4, and so is of use for our non-Continental readers.  It uses the solution to the crossed ladders problem, and requires one more fold than Egor's method but fewer than the method of Hagen von Eitzen which also works for any aspect ratio.

Fold the paper in half along the long side (constructing segment $EF$ in the diagram below, connecting the midpoints of $AD$ and $BC$).
Fold the paper along the segment $BE$.
Fold the paper along segment $AC$.

One can show that $GH = \frac{1}{3}AD$, so folding the paper along segment $IJ$ (and then either folding again at the crease, or folding along the segment $DF$ to get another intersection point) will produce the desired fold into thirds.
If the ratio $AB/AD = \sqrt{2}$ as in A4 paper, then we have $AC \bot BE$ (the converse is also true) allowing the omission of steps 1 and 2 that construct $BE$, and we can proceed as in Egor's solution.