If you're looking for a unique computer that throws away all the traditional PC design conventions, you might want to check out the Enlighten, a custom-made wooden PC from Suissa.
The visually dynamic style of the Enlighten explores the modularity of technology and "reflects the movement through time that our memories occupy and provides a tangible home for them."
The PC packs a micro ATX motherboard, Intel Quad core CPU or AMD X2 6400+, single NVIDIA 8800GTX video card or ATI Radeon HD2900XT, 4GB PC6400 memory, 1TB hard drive space, DVD burner, 620w power supply.
Heat is dissipated through the use of aluminum around the power supply and DVD drive and through "careful venting of air into, around and out of the main housing." Suissa says they avoided the cascading heat effect found in many computer designs by separating the power supply and DVD out of the main housing.
Want something more traditional? See Dell's green eco mini PC: