Saw these guys at work, and again at SIGGRAPH, showing what they did with free open-source animation software (Blender).
Funky thing is, you can browse their entire production repo here. This is wonderfully informative from a production management standpoint, as it shows how one group of guerrilla animators organized their stuff. You can even download the entire 200 Gig studio backup! Now that's what I call Open Source: even their techniques are transparently shared. The bigwigs here in Hollywood could learn a thing or two. Alas, we still barter in the antiquated currency of "ideas", as if a simple idea can make or break a film. Part of Catmull's keynote at SIGGRAPH addressed this issue. At Pixar, they build teams, and teams are their currency. Ideas are worth nothing in the hands of an inept team, but a good team can wrangle the gold out of any old idea. To reiterate: ideas are worthless. So we should all quit hording them. Let's open-source knowledge! It's the rising tide lifting all ships thing.
So here's the meat of this post: you need software. From the results of Big Buck Bunny it appears that free animation software has come of age. Put this with my previous post on production tools ("How do You Manage?") wherein I list free ftp services and the like, and you have a 100% no-overhead production. Except, of course, for the emotional overhead of sleep loss, eye strain, loss of family and friends from your withdrawal into the long-hours world of computer animation; not to mention all the hardware to purchase and maintain. But hey, nobody said filmmaking was easy; if it was, everybody would do it.
If you have a few ducats to spend on your labor of love, however, you can make your life much easier. In the following posts I will provide a rundown of the barebones software you'll need to think about when contemplating creating a CG film.
First: decide on the 3D app. This will serve as the hub of your data pipeline, so choose wisely, as it will effect all your subsequent decisions. The big contenders include the aforementioned Blender (pluses include that it's free and seems to be well-supported; the minus is there's not a huge existing base of users so expect a learning curve). For a small investment look into Animation:Master - you can get a web-based license for 50 bucks a year! It is purported to be oriented toward character animators - rare for cheap-end 3d software. Next step up would be Maxon's Cinema4d. Still cheap, although how cheap is hard to discern since they don't list pricing on their website. The brag the fastest renderer in the biz, and they have the schweetest 3d paint system with full Bodypaint3D integration. Some award-winning shorts have been done with it, but I don't know much else. At the next pricing tier we move into the ones aimed at the professional market: Lightwave3d, SoftImage, 3dsMax, Maya and Houdini.
Lightwave3D has excellent modeling and lighting tools, but with character animation tools that leave something to be desired.
For a higher price point, you can try Houdini, which is the de facto standard for visual effects, so it would be the appropriate choice if you have an abstract or effects-laden project. The downside is, again, weak character tools. Also a big learning curve. The full version is pricey, as in 8 thousand dollars -ish pricey, but you can get a stripped down learning edition for free, and a watermark-free version for only 99 dollars!
Next there's Softimage. I always forget about Softimage (almost forgot to include it) which is a shame because it is as full-featured and easy to use as any other, but for some reason hasn't caught on big in the industry yet (they were late arriving in the game with their XSI version, by which time most companies had gone with Maya). Comes in a variety of price points ranging from 6000-ish to a 500-ish educational version.
Lastly, I'll talk about the two I recommend for most serious projects: 3dsMax and Maya, both from Autodesk. Max is the industry standard in games, Maya the same for films, but they crossover everywhere so don't focus on that. From extended personal experience in the two apps, I'll say that Max trumps Maya in the realms of modeling and layout, whereas Maya is better for character rigging and animation. Neither has the best on-board renderer so they both rely on mental ray to be their "full featured" renderer - so I'd say that's a draw. Maya is more configurable and transparent, so it's better for those that like to drill down into the guts of the software; this is also its drawback, as it has the steeper learning curve. Max has a more logical interface, and lots of funky built-in effects and dynamics. Maya has Paint Effects, which is not comparable to anything else in any package. In the end, it's somewhat of a draw. Even price-wise, they have similar versions, and the obligatory free version for learning. I'm not going to start a flame-war by picking my favorite of these two giants: download the free versions of each and decide what's right for you. Alright I'll tell you: Maya. And Netflix is better than Blockbuster.