It’s pretty important and helpful for everybody to do a regular google-check for the owned domains. So take a closer look at the following google search parameters and you should get an quick idea whether everything’s running ok on your sites. I suggest you to play around with the parameters and try to combine them in different ways. Feel free to add missing paramters in the comments please.

get info about your domain:
info:domain.com

see links pointing to your domain:
link:domain.com

search keyword only in your domain:
keyword inurl:domain.com (allinurl for just a single keywords)
allinurl:domain.com keyword (allinurl for more keywords)

keyword search only in your domain:
keyword site:domain.com

keyword search only in a toplevel domain:
keyword site:.com

search keyword only in defined filetype:
filetype:pdf keyword

get a certain document from the latest google cache:
cache:domain.com/site.html

get a contentual explanation for a certain keyword from google:
define: keyword

get keyword result from a domain and exclude result from www.domain
site:domain.com -site:www.domain.com keyword