Whether you like your dining chairs to have arms or not is entirely a question of preference. Some people prefer to have more room for movement while eating, and in this case an armless chair is appropriate. Other however, like the armrests as a place to support their elbows while eating.
Dining arm chairs:
Dining arm chairs example. Pictured: Nuevo Living – Caitlan Dining Armchair in Tan Walnut
Also of interest: Sorrento Dining Arm Chair by Coaster; Set of 2 Dining Arm Chairs Mission Style Medium Brown Finish by Coaster; Set of 2 Dining Arm Chairs Wenge Finish by Acme Furniture.