There is no-doubt that there are many projects for the Raspberry Pi 3 but by far the best or at least the most fun is to build a home theater system.
Yes you can build a web server or setup a VPN which are very useful but to be able to stream your favorite movies and TV shows from a video library or from online is something that can bring hours and hours of entertainment.
I have been building entertainment systems with the Pi since the B+ model which did work but could be a frustrating experience.
The RasPi 2 did a better job but still would lag at times and buffer online streams.
With the Raspberry Pi 3 the the hardware has finally caught up with streaming video content that has made the viewing experience very nice.
There are several ways to go about installing a media center on the Pi but the best in my opinion is Kodi.
What is Kodi?
Kodi is a free open source media player that has a large community.
Kodi by itself is nice media player but the thing that makes it stand out is the ability to have Add-ons installed which can extend its functionality.
Add-ons are like apps for a smartphone with the most popular ones for streaming video.
The add-ons like Kodi are all free and maintained by the authors.
The most popular add-ons are Exodus, 1Channel, and Phoenix among others.
Other plugins are also available such as music, pictures, and programs.
If you have never tried Kodi or have in the past with a less than optimal experience than definitely give it another try.
If you have a older Raspi 2 Kodi can be installed and used but it will freeze sometimes and the controls will not be very responsive.
The new RasPi 3 also has built in WiFi and Bluetooth which works great with Kodi.
While the WiFi range is limited in range Kodi automatically will install the drivers.
The built-in Bluetooth is also nice and very handy when using a remote control or Bluetooth mouse / keyboard.
Whether your looking for a fun project or a good hardware platform for Kodi the new Raspberry Pi 3 is a good option.