A healthy tree in bloom stands for strength, a thin one indicates bad luck in life. Falling from a tree implies you may lose something, but it can also be a warning to let go of wrong attitudes and convictions.
Climbing a tree is a sign for personal ascension and success.
Shaking a tree is lucky, especially if it's bearing fruit.
Seeing its roots shows a connection to earthly goods and material wealth - are they spread out (openness) or do they go deep (reservation)?
The tree's trunk may give clues to your personality - is it rough (rough) or smooth (elegant)?
In my mind, trees stand for a connection to all life. They show the circle of the seasons, engage in symbiotic relationships with the bio-system around them, they harbor birds' nests, grow food, and they also grow old and wise. To me they symbolize learning and realization of potential; a cool place to rest under their rich canopy; various branches to explore, climbing higher and higher for exquisite vantage points. Being flexible and bending in the wind is as important as digging roots for nourishment and stability.
I just realized - I love trees. :-)