The methods of registration you provide define your addressable market of users.
Whichever option you provide your users, you are hoping for two things:
- They actually have that sign in method.
- They trust you with having access to the method they choose.
Do they have the sign in method?
Think about your market of users and if they'll have these methods. These are some generalizations based on my experience, so be sure to verify with data.
Facebook (1.44b MAU as of Mar 2015): Extremely popular in the US, western Europe, and pretty much the rest of the world. Basically inaccessible in China.
Twitter (302m MAU as of Mar 2015): Popular with a portion of people around the world (again, not China). This tends to be a group that's highly tech literate and, dare I say, into self promotion?
Google (2.2b users as of Jan 2015): Popular around the world (not China) thanks to Gmail and Android. If your product is on Android, offering Google sign in is a certain way to give the user a method they already have.
Email (~4b accounts as of 2015): Popular in developed markets. In my experience, people in India, China and emerging markets largely do not use email or in a far less frequent way than a Western adult or student. Even in the US, young people use email far less than working adults.
Mobile Phone Number (6.8b users as of 2013): Universally popular. More people on Earth have a mobile phone than a toilet (6.8b vs. 4.5b). If your user has a phone, they can auth with their number. See Twitter Digits.
Do they trust you?
You could do a survey of a group of potential users to get a sense of what they think of the options you're considering. Anecdotally, although Facebook is extremely popular around the world, trust issues persist with connecting a new app with Facebook. What will this new app do with my social graph? What will they post to my feed? Etc.
A concern, for some users, with email could relate to getting spammed.
Do they need to create an account right away?
Creating an account, regardless of method, is a big conversion barrier. Is there a way to let the user experience your app before they create an account? Wufoo did this to great success by letting users build a form before creating an account. Twitter is also doing this now with content for the logged out user. When the experience sells itself, giving the option to invest in its use before account creation can be valuable.
How will you re-engage?
Email, SMS (more so in emerging markets) or push notifications are needed for reengagement. Depending on the product, one may be more effective than the other. Consider how you'll reengage post-signup.
What do successful apps do?
Look around the space you're entering and see how the successful apps handle this problem. Then, look at other products that have accumulated massive amounts of users (WeChat, Whatsapp, Instagram, Facebook Messenger) and see how they handle it. Maybe you can introduce some new thinking into your market and differentiate yourself.
One last thought: Interestingly enough, Facebook decided to not require a Facebook account for people to sign up with Messenger. What auth method do they provide as an alternative? Mobile phone number.