For my own gmail account, I have multiple email addresses associated with it. For example, I have an email address from my university that is associated with my gmail, and I can send emails from my gmail as if they are coming from my university email address.
I'm reading up on the Google APIs, and I see that I can get a user's gmail address, but can I also get any other email address that is associated with their gmail account?
When a user logs in to my site, I'd like to present them with a list of the gmail-associated email addresses and let them select the one they would like to use.
EDIT: Thanks everyone for the answers, but I don't think any of them answers the question. I've been playing with Google's OAuth playground. It is strange that I can get lots of very personal information (a list of a user's contacts and even received emails) but I can't get the user's alternative email addresses.
Your description is a little vague. Are you talking about send-as alias accounts or alternate email accounts?
Send-as Alias
Either way, you can interact with the send-as accounts here: Manage Send-as Alias
Alternate Emails via Admin SDK
Federated Login
Also, I'm not exactly sure how you are trying to incorporate this functionality into your site but another area I recommend checking out is Federated Login for Google Account Users. This might also provide you with the functionality you seek.
Using federated login (also known as federated identity), your website or application can allow visitors to sign in using their Google user accounts. Federated login frees users from having to set up separate login accounts for different websites, and frees you from the task of implementing login authentication measures.