While there are lots of high level information out there about what you can expect with the Newsfeed in SP2013, I have not been able to find a list of the types of updates you can expect to see on the Newsfeed. After a couple of days of experimenting, my findings are as below.

Many thanks to @tbasrai for helping me out with the investigation.

Following a person

Your Newsfeed will show when the person you have followed does one of the following:

1. Posts a new microblog message or replies to a microblog conversation
2. Posts a new topic in a discussion forum or replies to a topic
3. Likes a discussion forum topic or reply
4. Gains a new reputation
5. Follows another person
6. Follows a document
7. Follows a site

Your Newsfeed will NOT show when the person you have followed does one of the followings:

1. Creates, updates or deletes a document
2. Updates their Ask Me About or Mobile Phone
3. Follows a tag
4. Is @mentioned by someone else
5. Likes a microblog message

Following a #tag

Your Newsfeed will show when the #tag you have followed is:

1. Used in a microblog message or a reply to a conversation
2. Used in a discussion forum topic or reply to a topic (in Body field only)

Your Newsfeed will NOT show when the #tag you have followed is:

1. Used to tag a document, page or list using the Tags and Notes button on the ribbon – (This is the biggest shortcoming for me!!)

Following a site

Following a site allows you to post microblog messages to that site’s “local” Newsfeed. You can select the site to post microblog messages to as seen below:

The site’s Newsfeed is explained in more details here: http://radutut.wordpress.com/2013/02/01/following-sites-in-sharepoint-2013/

Below are my findings of what happens when you have followed a site:

1. If you selected to post to that site’s Newsfeed, your microblog messages will appear on that site’s “local” Newsfeed
2. Microblog messages posted to that site’s “local” Newsfeed will appear on your MySite’s Newsfeed
3. If a microblog message is posted to that site’s “local” Newsfeed, and you have NOT followed that site, and the message IS tagged with a #tag that you have followed, then the message will NOT appear on your MySite’s Newsfeed.
4. If a microblog message is posted to that site’s “local” Newsfeed, and you have NOT followed that site, and the message @mentioned you, then the message WILL appear on your MySite’s Newsfeed.
5. You cannot @mention a site that you followed. This means you cannot post to multiple sites at once.
6. If you have followed a site, but the site does not have the Site Feed feature activated, then you will not have the option to post a microblog message to that site. The option will simply not appear on the list.

Following a document

Your Newsfeed will show when the document you have followed is:

1. Updated

Your Newsfeed will NOT show when the document you have followed is:

1. Deleted
2. Tagged using Tags and Notes

@Mention

Your Newsfeed will show when you are @mentioned in these scenarios:

1. @mentioned in a microblog message or reply to a conversation. Clicking View Conversation in the Newsfeed works fine.
2. @mentioned in a discussion forum topic or reply to a topic. Clicking View Conversation in the Newsfeed resulted in an error for me (thread has been deleted or something similar).

Discussion forum

Replies to your discussion topics are NOT shown on your Newsfeed. However, in the Newsfeed settings section of your profile, you can elect to be notified by emails when replies are posted to your topics.