I currently am in such a job. I'm doing a very diverse range of things, from schematic and layout design to web programming (although I do the latter rather dreadfully). It is a fairly large company and not my ideal job, precisely because it is in a large company, where everything is slow and bloated. An guy I used to work with a another company was employed here; he recommended me to his boss when he heard they needed someone with my skills, they called me for a quick discussion and offered me the job.
I also had a similar job in a startup company a while back. It really was my ideal job. Bad business decisions strangled it after about two years, unfortunately. I landed that one via the boring route -- job ad on a website. Applied, went to interview, got the job.
One framework I think is helpful is this: http://www.iwillteachyoutoberich.com/blog/ask-ramit-how-do-y...
Talking with people about what a job actually entails, versus what the job posting says it does, seems really obvious when you say it, but sometimes obvious things need to be said. During my last job search I actually talked with people on my options, and found it extremely insightful between what I thought the job was and what it actually is.
I'd highly recommend against working for a company that doesn't value a subset of your skills more highly than the others; a somewhat specialized position will pay better.
I would also highly recommend that you work for a company (or many companies) with vision, mission, and values that you connect with strongly.
This statement is extremely important. You can walk through hell if you're in good company. If you end up working with on great technology with people you can't stand, you will not make it through your job. The opposite will generally lead to your work environment being a lot healthier for you.