Developed in 1928 by Otto Diels and Kurt Alder, the Diels-Alder Reaction is an extremely important reaction for synthetic organic chemistry. It is an addition reaction where a conjugated diene reacts with a dienophile in a pericyclic reaction involving the simultaneous movement of 3 bonding electron pairs. The Diels-Alder reaction find common use among synthetic chemists because it is a regioselective and stereoselective means of creating a cyclic or bicyclic molecule. Diels and Alder were awarded the Nobel Prize for Chemistry in 1950.

A Typical Diels-Alder Reaction:
All carbons explicitly marked for clarity
  1,3-Butadiene                  Cyclohexene
      C           Ethene           C
    //            C              /   \
    C             ||            C     C
    |       +     ||     =>     ||    |
    C             C             C     C
    \\                           \   /
     C                             C

Thanks to vuo for constructive critcism/corrections, I'll try to expand on this later once school lets up enough.
In the meantime, Kurt Alder's Nobel Lecture describing the reaction in more detail can be found here: