I recently went through a Google interview and wanted to contribute the questions I faced.
Note: Google has apparently changed its interview slate, there weren't any system design interviews and all are coding questions. Might have to verify this clearly with your recruiters.

Round 1:

https://leetcode.com/problems/single-number-ii
Round 2:

https://leetcode.com/problems/decode-string
Round 3:

Given a tree representation of a html parsed output, wherein every block is a node in the tree, find if two html docs contain the same text.