The 14 Different Types of Convex Pentagons that Tile the Plane
Many thanks to Branko Grunbaum for assistance with this page.
An article by Doris Schattschneider about pentagons is available here.  Her interactive tiling page is here.
John Savard has put together a beautiful page about a pentagonal tiling system originally discovered by Kepler here.
Bob Jenkin's half-bath has a beautiful tiling based on the Hirschhorn Medalion.  This is one pentagon in the Chaos Tiles.
Bob Jenkins and Mike Korn have both made pages about non-convex pentagons.
Marjorie Rice has a page here.
Type 1 : D + E = 180
Type 2 : C + E = 180, a = d
Type 3 : A = C = D = 120, a = b, d = c + e
Type 4 : A = C = 90, a = b, c = d
Type 5 : C = 2A = 120, a = b, c = d
Type 6 : C + E = 180, A = 2C, a = b = e, c = d
Type 7 : 2B + C = 360, 2D + A = 360, a = b = c = d
Type 8 : 2A + B = 360, 2D + C = 360, a = b = c = d
Type 9 : 2E + B = 360, 2D + C = 360, a = b = c = d
Type 10 : E = 90, A + D = 180, 2B - D = 180, 2C + D = 360,
a = e = b + d
Type 11 : A = 90, C + E = 180, 2B + C = 360, d = e = 2a + c
Type 12 : A = 90, C + E = 180, 2B + C = 360, 2a = c + e = d
Type 13 : A = C = 90, 2B = 2E = 360 - D, c = d, 2c = e
Type 14 : D = 90, 2E + A = 360, C + A = 180, B + D + E = 360,
2e = 2c = a

Types 1-5 were found by K. Reinhardt in 1918.
Types 6-8 were found by R. B. Kershner in 1968.
Type 10 was found R. James in 1975.
Types 9, 11-13 were found by M. Rice in 1976-1977.
Type 14 was found by R Stein in 1985.

Sources:
The Penguin Dictionary of Curious and Interesting Geometry, David Wells, 1991.
Mathematical Recreations: A Collection in Honor of Martin Gardner, David Klarner, 1981.
Tilings and Patterns, Branko Grunbaum and G. C. Shephard