In short, Dr. House rules but Dr. Cuddy has clearly been gaining on him. Then comes Dr. Brennan closely followed by Agent Booth, both steadily increasing in search volume but distinctively behind the two front runners—just like the shows themselves, I guess. Google Insights for Search also provides us with country-specific breakouts and rankings:
While the House M.D. characters are most popular in Mexico, the Bones ones are in the US. Overall, House M.D. is more an international phenomenon than Bones. I take it this must be due to the latter not being broadcast in so many countries. Bones characters' regional interest is odd: hardly any European countries make into the top 10 but, for instance, Zimbabwe, Zambia, South Africa, Yemen, etc. do.