In what words is "s" pronounced like the English "z"?
It certainly seems to be in misma/mismo and desde. . .are there any others?
And on the same topic, is the "z" always pronounced like an "s"?
In most Spanish words, the 'S' and 'Z' are pronounced identically. They are usually pronounced like the 's' in 'side', kind of like a hissing sound. However, when an 's' is before a(n) l, n, m, d, b/v, or g, it is pronounced with a slight buzz, like a 'z'. Don't stress the sound too much though.
Here are some I could think of: isla, presidente and musica
So it's basically the same as the rule for pronouncing the "s" in making plurals in English, except the determining consonant comes after instead of before.
The unvoiced sibilant (sound of "s" or, if you use the seseo, c/z/s) is replaced by the voiced variant (becomes voiced) before any voiced consonant. For a list of the voiced consonants, see Chililover's response.
There are probably tons. Rasar comes to mind.
No, 'z' sometimes can be pronounced as a 'z' or as a 'th' I believe.