Embedded processors are highly optimized products. When you just want a good general use processor, sifting through the many options to find the best one can be daunting. Below are some excellent general-purpose use platforms that I recommend for academia. Are there other options, you bet. These are the best in class, most popular and great for learning.
This is a great starter board! It's cheap($12.95), yet powerful and can be used in a wide variety of applications. All FRDM- boards are pinned out in the Arduino shield standard so you have lots of expansion options. The FRDM-KL25Z can be programmed with the normal 'industrial strength' IDE you can also use mbed.org which sets it apart from many other products in this list for ease-of-use.
Made by PJRC. For those that want to put a high performance 32-bit MCU on a breadboard. Also, per the PJRC website you you are able to use the Arduino IDE. The hardware is about as bare-bones as it gets, but the nice small footprint and breadboard ability gives you lots of flexibility to add your own custom I/O.
The Tower System is another platform with a multitude of options. With the Tower System you get access to much more I/O and is designed with higher performance applications in mind. The particular variant I most often recommend is the TWR-K60D100M simply because it has so many features all packed in. USB, Ethernet, Crypto engine, CAN, SPI, I2C and the list goes on. Couple that with plenty of processing muscle with a Cortex-M4 CPU running at 100Mhz.
The Cortex-M series is primarily intended for embedded control applications. Whereas the Cortex-A series is built for graphical and multimedia applications. Wandboard.org has been getting a lot of attention in the community as a Rasberry PI, Beagle Bone alternative(comparison chart). Another similar product, still in development, is UDOO so stay tuned for that one.