The dictionary you quote is perfectly accurate; "I would think", etc., is used in situations where you are expressing an opinion without being too sure about it. The difference between these two sentences is one of nuance:
I think he's about fifty.
I would say he's about fifty.
The first suggests that you have some grounds for your opinion, and the second that you're more or less guessing. See this earlier question for a further discussion.
It should be noted that you would think doesn't mean the same thing at all. If I say:
You would think that the bank could figure out a more secure way to allow customers to transfer funds between accounts.
what I'm actually saying is that the bank has not figured out a secure way to handle fund transfers, and that this is unexpected. Unlike I would think, which is in the nature of a guess, you would think states something contrary to fact.