Today AVR and PIC are probably the most common microcontrollers among hobbyists. Both have a very wide range of device variants and both can be used to achieve similar results.
For a beginner I would suggest AVR due to various reasons:
AVR family (tiny, mega) is coherent and easy to understand. The architecture is powerful and modern, and is especially suitable for C compilers. AVRs can of course be programmed in assembly too.
Due to its C-friendly architecture, there are quality C compilers available, both commercial and free. The ubiquitous GCC is ported to AVR and called avr-gcc.
For getting started all you really need is a handful of basic components, the AVR chip itself and a breadboard. Even the programming cable between PC and AVR can be built essentially for free (a so called wiggler). However, several commercial development kits are available, most notably Atmel's own STK500. A commercial development kit is more expensive way for getting started, but doesn't require practically any prior knowledge about electronics. Some development kits contain for example LCD displays so it's easy to get interesting stuff done.
It has a rich hobbyist community.
PIC is notorious for its peculiar architecture. Many love PIC for this, some hate it. AVR is more straightforward and doesn't seem to cause as much extreme and polar opinions.
Both AVR and PIC are used in many serious commercial applications. However, they are not the only options of course. My personal favorite microcontroller for both hobby and commercial work is Silicon Laboratories' C8051 family, most notably C8051F530. There is an excellent free C compiler and assembler for the C8051 family called SDCC.
Summary: There are lots of options, but please don't let that overwhelm you. Just pick one and start learning with it. Microcontrollers are, really, surprisingly easy to master once you just decide to get going!
