At any medium-large studio (including games, TV, or feature films), an animator is hired to animate. Not to create textures or model characters or light scenes. Most bigger studios recognize that these are all skills that take decades to truly master, and that the true path to beautiful imagery onscreen is to fill the studio with expert specialists.
In other words, most studios aren't too hung up on finding people who "know a little about a lot of different disciplines." Most features and games studios are looking for an artist who "knows a LOT about ONE discipline."
It's the pairing up of these experts that results in the truly memorable work you'd see in any blockbuster film or A-list game.
Of course, there is nothing wrong with dabbling in all the different disciplines available to you as a CG artist, but we generally recommend that once you've found which discipline you are the most interested in - be it animation or modeling or lighting or rigging or textures or whatever - once you've found your "true calling," your best bet is to put the rest of that stuff aside and focus as much time as humanly possible on becoming a true expert in whatever that chosen field is.
Many people will say that this will limit your job opportunities, and guess what?
They're right. It will.
But I guess it boils down to you deciding what kind of job you are looking for, and what kind of career you are going to attempt. There is nothing wrong at all in deciding to be a generalist, and continue to learn about all aspects of this stuff called Computer Graphics. There are many jobs, especially junior-level jobs at smaller-to-medium-sized studios, where generalists are specifically sought out and encouraged.
However, I can't tell you how rare it is for a generalist to get a job as an animator at a major feature studio or large game studio. Almost every professional animator at that level has decided to focus at least MOST of their time on animation, even if they also enjoy other disciplines deep down...
Before I end that thought, though, it's really important to point out that if you are new to the industry, getting a junior job as a generalist can be one of THE best ways to break into this business.
Getting your foot in the door of a studio and getting *any* kind of professional experience is invaluable, and will help you make connections, learn the ropes, meet people to learn from, and look great on your resume.
If you aren't getting to spend most of your time at work actually animating and growing as an animator, then my advice is to work hard, do a great job, and then go home and animate your brains out and practice as much as you possibly can in your spare time. Read animation books, get involved in online animation communities, meet up with some animation student friends and watch some animated films frame-by-frame and talk about what you see...
Getting a job where you aren't doing *exactly* what you hope to be doing doesn't mean that you have to stop striving towards your dreams of working as an animator! It's more than common for animators to have to work their way up, and slowly climb that ladder until they finally get their dream job.
It's very rare for that to happen overnight, so don't automatically turn your nose up at jobs that aren't exactly what you hoped for... Just don't let that job stop you from continuing to move forward!
- Shawn :)