Is there common ground between the Tao Te Ching and Buddhism?

In the Dao De Ching it is stated that:

"Therefore it is said: He who desireless is found The spiritual of the world will sound. But he who by desire is bound Sees the mere shell of things around."

One whose mind is filled with desire only sees the surface of things as they really are. A mind filled with desire sees the world as something to be controlled and used as tools or means for achieving one's will. And so, the mind does not understand that nature, in its deep mystery, is beyond the scope of language and reason.

The world does not need to be controlled, but the mind to be tamed. The wise one understand the changing and ever flowing rhythms of nature, and let's him/herself to go with it: that is Wu-Wei, or effortless action.

Early Buddhism and Daoism (as expressed in the DDC) point to desire/greed and instrumentalization of nature/the world (as defined in SN 35.116) as the causes for unbinding with the Tao/Samsara.

Have a wonderful day!

Wuwei, as how I understand it, has these understandings, depending on the context:

• You do something because you are born for it and do it without wondering why you need to do or learn how to do it (e.g. trees produce oxygen not because oxygen is needed for animals, but because they need photosynthesis)
• When you are doing it you are being present in the moment, and allow life to lead you to something unexpected, yet you do not get confused and unprepared when the unexpected occurs
• Your action has been simplified to its most basic parts so it can be accomplished in the most efficient and effortless ways
• You don't need to do anything because you see the order from the chaos, and you see the big picture from above
• You do something impossible or insane with confidence and fearlessness, because you have the knowledge (e.g. sailing into a storm with a smile)

Therefore, I think while Buddhism is about avoiding attachments to not having sufferings, Daoism is about attaching and having no suffering at all.

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.

I've read that one of the things that Taoism and Buddhism have in common is a sense of the ineffable. The opening lines of the Tao Te Ching go

The Tao that can be spoken is not the eternal Tao. The name that can be named is not the eternal name

meaning perhaps that the Tao is beyond words so everything that you read about it ... well that's not the real thing.

Contrast that to the Flower sermon where the Buddha does talk and instead just holds up a flower. When he did this ...

The disciples were greatly confused. Buddha quietly displayed the lotus to each of them. In turn, the disciples did their best to expound upon the meaning of the flower: what it symbollized, and how it fit into the body of Buddha’s teaching.

however Mahakasyapa understood and smiled. The Buddha said

“What can be said I have said to you,” smiled the Buddha, “and what cannot be said, I have given to Mahakashyapa.”

So again beyond words.

I don't think it is too much of a stretch to see the Taoist influence within this Chineses Buddhism sutra. Certainly if it isn't a direct influence then it is something that the two religions had in common.