I'm going to assume you understand why Twitter rocks and talk about where Google and Twitter intersect synergistically.
Here are the 11 coolest gadgets and devices I could find that combine two of the coolest internet phenoms, Google and Twitter. And yes, I said cool three times already.
Twitter/Google Maps Mashups TwitterMap - the most flexible and powerful of the three. Gives you more control than TwitterVision. TwitterVision - shoots you around the world in real time as people tweet. More entertaining than TwitterMap. GeoTwitter - shows how much cooler the other two are.
Search Twitter with a Google Custom Search TwitterSearch - can add it to you Google homepage.