When do I use "parere" and "sembrare"?
I'd like to see some examples of common usage so I can get a handle on what the differences are, if any.

Question

Answer

Parere and sembrare are largely, if not 100%, synonymous. One might say that maybe "sembrare" is slightly higher register than "parere" which is sometimes more emphatic.
Moreover "parere" is also a noun, that means "opinion", "thought about something", e.g.:
Dammi un tuo parere = give me your opinion

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