Can I put Debian on my Rasberry Pi?

Yes.

Debian armel will work (with a custom kernel), but will not make best use of the floating point hardware. Debian armhf will not work (see below).

Generally, your best bet is to use Raspbian - which is (mostly) Debian armhf rebuilt by members of Debian for the RPi's ARMv6+VFP2 ARM variant. Raspbian releases usually follow the corresponding debian release but do deviate in a handful of cases for various reasons.

Be aware that the raspbian images distributed by the raspberry pi foundation contain additional packages supplied by them including updated versions of some software and the addition of non-free software including Oracle Java and Wolfram Mathematica.

Should I buy a Rasberry Pi?

That is a decision that you will have to make given your application, below are some pros and cons that you should consider.

Pros:

Cons:

A number of similar boards are available, generally at slightly higher prices but also usually with more powerful processors. Some examples are given below, more can be found in the FreedomBox targetted hardware list.

Raspberry Pi issues

The Raspberry Pi issues relate to technical problems, software freedom and hype:

Binary blob needed to boot

The binary blob needed to boot the Raspberry Pi can be downloaded using the rpi-update script available from https://raw.github.com/Hexxeh/rpi-update/ . It can be used with vmdebootstrap to create a botoable SD card image, according to a recipe from Petter Reinholdtsen. No known effort to reverse engineer the blob is known 2013-10-30.