I would like to search small claims court cases by name of defendant in several locations in the USA. Is this possible? How could I go about doing that? Is there a website (free or paid) that does this?
In some jurisdictions you will be able to view the docket (docket number, filings, etc.) of any case; however, if your question pertains to verdicts, those are not published. Not for small claims, nor any district court matters. Some jurisdictions don't even publish superior court verdicts, except those where the district court appealed to the superior court for an appeal or ruling en banc relating to an issue of procedure. Nearly every state will post their Law Court cases. If docket info is all you seek, go to the court's website, and if they have it there will be a link or searchable database.
If it is verdicts you are looking for, you will need to research either the old fashioned way (go to the court, view the case file and if you want copies, have cash or check ready for anywhere between $1 to $5 for the first page with each additional page running anywhere from .50 to usually a dollar or two. Or, you can pay to use a background search service like Intelius to do it for you.
It's going to vary by state and county. The technical capabilities (fueled by budgets) of the court will dictate how much information is searchable online.
Your best bet is to do some internet searching for the state or city name and terms like docket, filings, electronic.
If you have a specific locality, update your question and perhaps someone can give you the exact URL.