In what situations should a SAAS company offer phone support? In what situations should it only be email support?

Offering easy and quick access to your support team is one of the best ways to delight your customers. Even if they have a question that can be answered via email, being on the phone with them gives you the opportunity to calm down a frustrated customer, provide solutions faster, and present a positive image of your business by being friendly, personal, and helpful. On top of that, as in marketing and sales, it's important to be present wherever (and however) they're looking for you, and if they're searching for a phone number on your website, only to find that you can't be contacted by phone, you're likely setting them up for an even more negative experience than the one they were already facing.

I would suggest looking at it from the perspective on what type of phone support is required in general depending on complexity of application and real-time access to information. For example, if the service is a SaaS based contact-centre solution, then you may need phone support for customer confidence/loyalty if they are worried about access or loss of data in real-time. If the service is more of an office productivity tool, then as the previous experts listed you need to look at the alternatives prior to someone having to pick up the phone (i.e. FAQs, manuals, discussion boards, on-line forms for various types of requests/feedback or even a LiveChat window).