Is there common ground between the Tao Te Ching and Buddhism? I am interested in Buddhism and the book Tao Te Ching, written by Lao-Tzu in c. 600 BC. Is there common ground between these two Eastern philosophies?

link to audio of Tao Te Ching
There is common ground. But there is common ground between Christianity and Buddhism, too. So...

A commentator of the Taoist philosopher Guo Xiang's work and a Taoist himself, I forget his name now (I can look it up) once wrote that - I paraphrase from memory - Buddhism and Taoism are diametrically opposed, because one seeks detachment from all existence, while the other seeks attachment to all existence. One seeks liberation by detaching from all phenomena, while the other seeks liberation by becoming one with all phenomena. The two paths seem to be the same, but really they are opposite.

Your question is broad, and so it's hard to answer. There are just too many sects... some Chinese ones like Huayan were influenced by Taoist philosophy so there is more common grounds... and then there are Taoist sects that were significantly influenced by Buddhism, like the Quanzhen School...

In the Pure Land tradition, the great patriarch Tan-Luan, was initially a Taoist teacher. He wanted immortality but couldn't achieve it. Then he met the Indian Bodhiruci who gave him the Infinite Life Sutra, and Tan-Luan was so delighted by this sutra that he burned all his Taoist texts and followed Buddhism alone. If this story is true, then we can say at least one person didn't think the two were compatible. Tan-Luan sought immortality, but it occurred to him that when Taoism speaks of immortality, it does so from a point of view of attachment to existence, while Buddhism's ultimate point is nirvana which is neither-existence-nor-nonexistence (suchness). Something far removed from existence and non-existence.