What happens if I cast Green Sun's Zenith while Grafdigger's Cage is on the battlefield?
Two important comp. rules here:

101.2. When a rule or effect allows or directs something to happen, and another effect states that it can't happen, the &quot;can't&quot; effect takes precedence.
609.3. If an effect attempts to do something impossible, it does only as much as possible.

So you'll search your library for a green creature cost with converted mana cost X or less, do absolutely nothing with it (since you cannot, due to Grafdigger's Cage) and leave it in your library, then shuffle your library, then shuffle Green Sun's Zenith into it's owner's library.
This allows you to shuffle Green Sun's Zenith into your library for G, which might be handy/relevant in some obscure case (possibly against mill decks?).