I am interested in everything related to this kind of effect (modeling, game engine, animation). What sort of stuff is needed?
Here are some sample images of what I mean:
Cel shading / Toon shading
There might be something more to it, but in general, all of your examples use Cel shading to some extent.
As for your question, whether there are any engines that support this. Well, that should be possible in every engine out there. The ones that aren't hobby projects should actually have such shader available in their standard assets (Unity3D has those dupped Toon shader).
But, the power behind the cel shading is shaders.
For 2D applications, using software rendering, you could achieve this by applying a per-pixel modification. That won't be nowhere near fast, but it's doable.
As for tutorials and guides, there are plenty (GLSL, HLSL), due to the release of Borderlands and huge amounts of Indie studios started the past years, the information available about cel/toon shading is aplenty.
There is a specific question on GLSL cel shader right here in GameDev.SE: Is there any opengl cel shading tutorial out there (without GLAUX)?.
A screenshot of Borderlands
That should be enough information to get you started with.