Quote: "Maybe Shrek was, but I heard Pixar makes their own software. They may use other software for animation and modelling, but they use Pixar Renderman for most of the rendering."
Dreamworks, Industrial Light & Magic (ILM), and Pixar all user Maya for thier Modelling requirements.
They all also use Pixar Renderman for thier Rendering Requirements. However this isn't to say that these movies are all exclusively developed using that software.
The Pixar Renderman software, is only available as a plug-in Renderer for Maya; however there is a stand-alone package that can be used.
Mental Ray is a very good render engine available (as default now) with Maya, Softimage | XSI and 3D Studio Max. When people saying 'well my 3d packages can render better than yours', most of the time they don't realise they're all using the same bloody render engine (so actually they all have identical features and render the same

)
Personally I've found for 3D Studio Max, SplutterFish Brazil and the new Rio (free version) are very good. Currently Liandri has a contract with Splutterfish, with thier Brazil R/S.
Also on the market renderwise is Messiah:Render, very pricey but it's one of the best systems you can get due to it's advanced lighting models and material designs.
Best on the market in terms of overall abilities, is Renderman. Simply because it uses Shaders for all of the rendering effects.. Mental Ray has been adding a similar system recently, but Pixar have had Shaders since day one (1989 Renderman was first released for Maya 2.. shocking how far we've come).
Though while that is it's greatest strength, that's also it's biggest weakness. It isn't newbie friendly... hell professionals have problems with it, becuase you need to be able to create shaders for EVERYTHING.
There are some basic shaders done now, but your still have to do stuff liek Global Illumination yourself, and such.
Though we can thank it because Renderman is the source of 'Hardware Shaders', which are used in every major game today. Thank god in a less complex mannor though. Still they're fairly similar.
In terms of packages doesn't matter much.
Anything that can output to a render engine can be used. Blender can even be used, utilising Yafray for crying out loud... so yeah the limit is on the artist not the package nowadays.
If everything else fails you can always create your animation as a machinima altering the render output, and depth of the shaders being used to highly complex algorithms.
Use something like Doom3 or Half-Life2.. output then add sound later. I mean after all it's all the same thing in the end.