It's faster, easier, and frankly, more reliable. DO NOT break up with somebody through email.
Email is the most impersonal of all forms of communication.
When it comes to something as intensely personal as a relationship, impersonal dismissals can hurt the most. Plus, it doesn't reflect very well on your caring nature. DO NOT ask somebody out through email. DO NOT try to solve arguments through email. No matter how eloquent your writing style may be, compassion cannot be expressed through email.