Can a shopkeeper refuse to serve you?

Answer 1

As long at it is not for a "protected" reason (race, color, religion, or national origin) any business can refuse to provide service to anyone without reason.

The "We reserve the right to refuse service to anyone" sign is not required though it does provide defense against complaint happy patrons.

Answer 2

In the USA The Federal Civil Rights Act guarantees all people the right to "full and equal enjoyment of the goods, services, facilities, privileges, advantages, and accommodations of any place of public accommodation, without discrimination or segregation on the grounds of race, color, religion, national origin,or disability."

A shopkeeper can however refuse you service based on numerous other reasons such as the most famous no shirt, no shoes, no service rule if it is posted. A shopkeeper can also refuse you service if you are in anyway being a nuisance or causing a disturbance in the esablishment such as using profanity, foul language, making obsecene gestures, harrassing staff members, disturbing other patrons, etc.