The following info was provided by John Cochran, with permission to re-post here.

A 3-way switch is a SPDT switch.
A 4-way switch is a cross-connected DPDT switch.
 
I'll call the 3-connections on a 3-way switch A, B, and C.
I'll call the 4-connections on a 4-way switch A, B, C, and D.
 
On a 3-way switch, A is connected to either B or C depending on the switch
setting.
 
On a 4-way switch, A is connected to either C or D depending on the switch
setting.  B is connected to either C or D (whenever one is NOT connected to
A at that moment.
 
 
First here is an example of a 3-way switch setup
 
   Switch 1    Switch 2
    +---+       +---+
Hot |  B+-------+B  |    +------+ Neutral
----+A  |       |  A+----+ Load +--------
    |  C+-------+C  |    +------+
    +---+       +---+
 
Switch 1 will determine which connector (B or C) is hot.
Switch 2 will connect the load to either a hot or dead connector.
 
Now for an example of a 4-way switch setup
 
    3-way     4-way     3-way
   Switch 1  Switch 2  Switch 3
    +---+     +---+     +---+
Hot |  B+-----+A C+-----+B  |    +------+ Neutral
----+A  |     |   |     |  A+----+ Load +--------
    |  C+-----+B D+-----+C  |    +------+
    +---+     +---+     +---+
 
Switch 1 will make either connector B or C hot.
Switch 2 will pass the hot connector to either C or D.
Switch 3 will connected the load to the hot connector.
 
You may use as many 4-way switches as you want to and any switch will
either turn on or off the load.
 
Example:
 
    3-way     4-way     4-way     3-way
   Switch 1  Switch 2  Switch 3  Switch 4
    +---+     +---+     +---+     +---+
Hot |  B+-----+A C+-----+A C+-----+B  |    +------+ Neutral
----+A  |     |   |     |   |     |  A+----+ Load +--------
    |  C+-----+B D+-----+B D+-----+C  |    +------+
    +---+     +---+     +---+     +---+

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