Install the utility named dsh:

apt-get install dsh
brew install dsh

Add the list of servers you want to work with to .dsh/machines.list in your home directory. It might look something like this:

web1.prod.domain.com
web2.prod.domain.com
web3.prod.domain.com
web4.prod.domain.com
web5.prod.domain.com
web6.prod.domain.com

Add this to your .ssh/config:

Host web*.prod.domain.com
  User your_username

Now you can do things like this:

dsh -Mac -- "tail -f /var/log/some_log_file.log"

Combine that with grep to look for certain things that you are logging:

dsh -Mac -- "tail -f /var/log/some_log_file.log" | grep "look for something"