Raspberry PI is a very powerful, small and cheap computer board. You can use it for several projects, many of which can be found in this blog (a selection is also resumed in Best Raspberry PI projects with Open Source software). There are a number of hardware pieces that can improve your RPI performance of add amazing features. Many of these can be bought with a very affordable expense and will be classified in this post by cost range.
Accessories up to 10$
Some CPU intensive applications can give you RPI hard days. In these conditions, having CPU protected from hot temperatures can assure a longer life to your loved board.
The most important part of Raspberry PI is its storage: SD card. Its importance is often underestimated and it can drastically boost your RPI performance. It is important to use at least a class 10 micro SD card
Correct power supply is another performance factor. Some people use common smartphone charger to power RPIs, but even if this could work for low load works, some applications could led to system crashes. Usually Raspberry Pi requires up to 3A (5V) power supply. Also a power switch is comfortable for powering on/off.
Some portable projects with RPI require a local display and/or a touchscreen to manage without an HDMI external display. Current technology allows to have a touchscreen with a very affordable price. And with a few more dollars it can be coupled with its case.
Having a RPI based Media Center is fantastic, but using TV audio outputs is somethimes not enought for most demanding people. Adding an Hi-Fi audio output can be a good compromise for high quality audio lovers
Sense HAT add your RPI environment interaction sensors. It is important when you plat to use RPI for IOT or home management projects, including Orientation, Pressure, Humidity and Temperature measurement capabilities with a single board.