As with so many things, this answer will vary as each state has its own rules and regulations for massage therapy.
In general, basic points such as the therapist washing their hands before and after each session and clean linens being provided for each client should be observed everywhere. Of course, there is much more to proper hygenic practices than that. Unless you are in one of the few states that don't require licensure, your state massage Board should have a listing of rules and regulations, including required hygenic practices. This can often be found on their website.
With this being a concern, you can always call ahead and speak to the therapist about this topic. Or, if you plan to visit a local spa, drop by and speak to a manager - they may even be able to show you a room. Online reviews of vacation destination spas may also provide some insight for those situations where you are traveling and seeking a massage.
You have every right to insist upon a clean room, clean table, and proper hygenic practices and many massage therapists are postively meticulous when it comes to cleanliness. If you aren't satisfied with one therapist's or spa's answer to your query, or practices, then seek out another.