Every card in the deck can be cast without paying mana in one way or another. There are a few different categories:
0-drop cards. These have no inherent mana cost.
Phyrexian mana (circle bisected with vertical line). Phyrexian mana can be paid with 2 life instead of mana.
Cycling.
Street Wraith has a cycling cost of two life.
Improvise. Tapping artifacts pays for the mana cost.
Convoke. Tapping creatures pays for the mana cost.
Affinity for artifacts. Cards with this ability cost 1 less for each artifact you control.