There are essentially two types of roots, taproots and fibrous roots:

Left picture:
This is a picture of the roots of Mirabilis hirsuta. There is one central main root, the taproot, that grows vertically downward. It is the primary root (developed from the radicle of the seedling). Taproots are often swollen, serving as storage organs for wintering.
Taproot systems are essentially found in the Gymnosperms and the Dicotyledons. Many vegetables have taproots, such as carrots and beets.

Right picture:
This picture shows fibrous root systems in a prairie. A fibrous root is a thin root arising from another root or from the stem tissue. The entire root system can be fibrous (with no root especially larger than the others), as in the case of Monocotyledons, where the primary root system is short-lived and the root system develops from adventitious root.