You can follow the advice on County Warrants Home Page to do a free warrant search, or you can pay for access to a database.
If you decide to go with a warrant database that you have to pay for, go with one of the better ones. Since Warrants are usually issued within counties, I recommend one that includes County Warrant information and a County Warrant Search. This is the best one I've found. It's geared toward City, County, and State Records:
Warrant Search Site
On the site that the link goes to, for an extra Ten Bucks you can upgrade to get their searching service for a year, so you can look up friends, family, and loved ones.
(As it turns out, my dog Riley does not have a Warrant.)