I sometimes use arduino for small projects, where designing a new hardware is not in the budget, or if you need a fast solution.
The software for the arduino makes it quite easy to access the features of the Atmel MEGA series microcontroller and the microcontroller itself is quite robust for minor misuse/errors in connections. And its 5V logic, so most of the cheap eletronic parts work with it.
The arduino software is mostly a wrapper for C, writing in arduino is like coding in C with some additions to make it easier to access the pins of the CPU.
(E.g. in C you would set an output pin with "PORTB=(1<<PINNUMBER);", in arduino it's "digitalWrite(PINNUMBER,1);").
To make it even easier, they changed the pin names, so you don't have to mind the different ports of the MEGA CPU.
For a lot of applications there are so called "shields", which you can plug onto the board to expand the capabilities, like driving DC Motors.
And its powered via USB, so for just fooling around with some leds and stuff you don't need an additional powersupply.
Get your self an arduino board (like the UNO-Board, take the normal one, not the SMD Version, incases you fry the CPU you can take it out and replace it for a few bucks) and a breadboard and some wires for it and you are ready to go. The breadboard wires fit directly to the arduino. Have fun. Bestway to explore microcontroller systems, I think.
Last note: If you goal has nothing with interfacing the real world (and i don't mean a screen, I mean motors, servos, LEDs, buttons, sensors and so on) then you better look for a different platform, as the arduino is not nearly powerful enough for "multimedia" applications.... If you need just a little more power and you are a windows user, take a look at
www.ghielectronics.com. It's like a more advanced (interfacing USB devices an so on) version of the arduino, but it is programmed in .NET.