The corners of my eyes are often dry and itchy. What can I do?

Eye exam. Check for angular blepharitis (lateral > medial corners). Look for evidence of allergies, secondary sources of irritation, or dry skin (eczema). Try some lubricating ophthalmic ointment, antihistamine for itching.
See your doctor. There are several potential causes of your irritation: allergies, dermatitis, infection, to name a few. Better than trying to treat the symptoms by yourself, you should have an eye doctor look for the underlying cause. This will provide you with the most effective treatment for your particular condition.