Yes, your customer(s) can have a major impact on what taxes you owe. Non-profits and certain resellers, for instance, may be exempt from sales tax. If you’re selling to someone from out-of-state, you will generally want to collect the sales tax from their state, as opposed to your own.
Because these things can get complicated – and because tax law is prone to frequent changes – it’s best to consult with a professional accountant to determine the tax liability for people who are purchasing from you.