The prefix co (and its alternative forms con, com, col and cor, depending on which letter follows the prefix) has the meaning with, together with.

A prefix is usually not followed by a hyphen. Some examples:
Afterthought, antedate, biannual, collaborate, commemorate, confederation, displace, ensure, illegal, indirect, overuse, posttraumatic, prepaid, replace, submarine, underestimate, uninterested.

So you are right in leaving out the hyphen in words such as cooperate, collaborate and coordinate.

However, in some cases a hyphen is to prefer, since otherwise the spelling might suggest a different pronunciation:

If you write co-opt without a hyphen (coopt), it looks as if it could be pronounced with a vowel as in too, and re-edit, when written reedit might sound like read it. The same pronunciation issue would apply to, for example, re-enter, re-establish, and re-examine.

Some words with the prefix re- have two versions, one with and one without a hyphen:

When you re-sign a document, you sign it again, but when you resign, you quit a job.
To re-cover means to cover again, while recover is to get better, regain your health.
When you re-store goods, you put them back in store again, but to restore something means to reconstruct or bring back to a former state.

You can read more about re here.

And, since we are dealing with English, we have to accept inconsistencies like the following:

Anti-clockwise, anti-hero and anti-Semitism but antirust, antiseptic and antisocial.
Vice President of a state; vice president or vice-president in business.
Viceroy but vice-chancellor.

A last note: Instead of writing cooperate, you could consider writing collaborate. There is a difference between the two!

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