This is going to be a long post but lots of info for you:
Free Books
http://www.dailyfreebooks.com/ (I get this as a daily email with only the category of books I'm interested in)
http://www.ereaderiq.com/ (I only use this when I'm bored, it's a good site but I rely on others for daily use)
http://fire.kindlenationdaily.com/ (When you go to this site, sign up for BookGorilla to get emails about books in your email)
http://ereadernewstoday.com/ (I used to use this one daily but when the format changed, it wasn't as useful to me.)
http://bookbub.com/deals/ (I get this as a daily email)
http://www.dailycheapreads.com/ (just found this one)
http://www.gutenberg.org/ (If your looking for classics)
Free Apps
http://www.dailyfireapps.com/ (free apps sent to you daily)
you can download your music to your Kindle (if you use “cloud” to store/backup your music from your computer you can download it to your Kindle)
Pandora is available as a an app
useful apps:
Adobe Reader by Adobe Systems (for reading .pdf's - Don't really think you need it...but..)
Book Collections (Kindle Tablet Edition) Digital Media Revolutions (great for simple book organization)
Collections for Kindle Fire (7" Fire Version) (Kindle Tablet Edition) Gagler Enterprises, LLC (for a more intense organization experience)
Free Kindle Books and Tips Gagler Enterprises, LLC (great blog with good tips)
OverDrive Media Console: Library eBooks & Audiobooks OverDrive, Inc. (allows you to search and download books from public library)
Pinterest Pinterest, Inc (if you have it on your computer, you should have it on your kindle – I think)
textPlus Free Texting for Kindle Fire/Fire HD & Android Phones, Tablets textPlus, Inc. (if you have access to Wi-Fi, this can be useful)
You can also use the Facebook app and any games you play on Facebook can be played from your Kindle.
Word of Caution: When you get free apps, try to take a quick look at the reviews. Sometimes, the reviews don't really matter, but sometimes the clue you in on whether this is a legit game (game, nothing else) or if it's a way to mine for your info (not cool). If you look at today's app offer from Amazon, you'll see what I mean. Looked like a cool game, but not with all the info they want.
Word of Caution: Don't “Allow Installation of Applications From Unknown Sources” - This can be found at: Use gear in upper right corner, press “more”, then go to “Device” and read down.