It turns out that if you assume that each new cut will cross all the previous cuts, you can determine the number of pieces without actually cutting the pizza. We note that as the knife enters a new piece, it produces one additional piece. Before the first cut, there is only the single pizza, but the cut produces one new piece. With the second cut, the knife enters the pizza (producing one new piece) and crosses the first cut producing another new pieces. When done in this fashion, with the nth cut, the knife produces n new pieces. So to get the total pieces we just need to sum the number from one to seven (plus one for the original whole pizza). This gives 29 pieces. Of course we need to show that cuts can actually be made in the prescribed method. This is shown in the diagram below (nobody said everyone got an equal piece). The red cuts are just to make it easier to count the pieces.

Pizza for Everyone