What makes sulfur-containing compounds such good antioxidants?
There are several factors that combine to make sulfur compounds such effective antioxidants.  First, sulfur compounds often contain S-H bonds (mercaptans) and are excellent radical scavengers because sulfur radicals are thermodynamically more stable than the analogous oxygen radical.  That is to say that the following equilibrium lies far to the right
$$\ce{ROS^{.} + RS-H &lt;=&gt; ROS-H + RS^{.}}$$
where ROS represents a "reactive oxygen species" such as hydroxyl radical ($\ce{HO^{.}}$), superoxide radical ($\ce{O_2^{-~.}}$, etc.  Sulfur compounds (sulfides and disulfides, for example) are also very easily oxidized to their corresponding sulfoxides.
$$\ce{R-S-R +ROS -&gt; R-SO-R + deactivated ~ROS}$$
If multiple mercaptan groups exist within a molecule (for example multiple cysteine residues in an amino acid) they can be oxidized to the corresponding disulfide while reducing an oxidizer. 
$$\ce{2~ RS-H + [oxidized~molecule] -&gt; RS-SR + [H-reduced~molecule-H]}$$
This oxidative process provides sulfur compounds with a second pathway to trap or transform, and consequently inactivate, ROS.

In addition to being very effective ROS scavengers, sulfur compounds also bind strongly to many metal ions.  These same metal ions often play a role in the generation of ROS.  By binding to them, sulfur compounds effectively remove them from the ROS generating process thereby further lowering the concentration of ROS in the cell.