Many view the story as a cautionary tale against continuously giving people things when they keep asking, causing them to just keep taking and taking while giving you nothing in return.
Others view the story as a Green Aesop, showing the consequences of when man continuously takes from nature while doing nothing to maintain it.
The Tree's love for the Boy is unconditional, but because the Boy is never said to give the Giving Tree anything in return, and doesn't seem to notice or appreciate the sacrifices the Tree is making for his happiness, some readers find the Boy to be very unsympathetic, which in turn makes the Giving Tree's sacrifice into glurge.
Some have even interpreted it as a story about an abusive relationship, with the Jerkass boy taking advantage of the tree's hospitality.
Tear Jerker: The story is (intentionally) both heartwarming and sad. We cry in happiness for the selfless spirit of the Giving Tree even though we feel sad that she has sacrificed everything about herself to express that love.