Yes, if you want a thick healthy looking lawn, you should mow your lawn once a week. Allowing your lawn to become over grown can cause your lawn to gain a lot of thatch, which will make it harder on your grass to grow properly. Maintaining around a 3 inch height is a recommend height for your grass to grow the best.
When ever your grass grows to around 3.5 + inches high you should mow the lawn. In the spring and fall your grass should be maintained at a height of 2.5-3.0 inches high and in during the summer your grass should be maintained at 3.0-3.5 inches high.