The strange shape seen in each of these Mahjong tiles is a fungus known as lingzhi. The lingzhi is known as the herb of immortality. The lingzhi resembles the head of a scepter, ruyi,  (seen here in wikipedia ). Michael Stanwick notes that the scepter was actually modeled after the fungus.

http://en.wikipedia.org/wiki/File:MS-SchnitzlackRuyiSzepter18Jh.JPG

The scepter, a symbol of nobility, also means "according to your wishes" thus the fungus means that too. (Patricia Bjaaland Welch, Chinese Art A guide to Motifs and Visual Imagery). Michael Stanwick adds "The fungus symbolism was transferred to the scepter and the scepter was often given to old men of renown or people of note. The idea being, I think, to confer longevity onto the recipient."

The fungus is seen with different plants, with two different plant groupings representing the four seasons:

top row: peony (spring) lotus (summer) the next tile may be grapes or a reader has suggested it may be a stylized chrysanthemum (autumn) and either a narcissus or camellia (winter)

bottom row: Plum (winter) orchid (spring) bamboo (summer) chrysanthemum (fall)

I have found while researching that some plants and flowers fall into two different seasons, but here the bottom row is the grouping of four plants, plum, orchid, bamboo and chrysanthemum known as the "four gentlemen" in Chinese art. Patricia Bjaaland Welch's book Chinese Art  A Guide to Motifs and Visual Imagery is an excellent resource for understanding symbolism on the tiles.

Here is a link to the Wikipedia article referring to the four gentlemen

http://en.wikipedia.org/wiki/Four_Gentlemen