Who owns your twitter account? Your employer?
The issue is a man who worked for a company, and had a twitter account named CompanyName_HisName (see the links below for the details). He tweeted on work hours for work purposes and had amassed 17,000 followers. Then he left the company and claims to have made an arrangement where he could keep the account so long as he occasionally tweeted stuff for the company. He changed the account name to just HisName (removing the company prefix) and thought all was fine until the company sued 8 months later. The company claimed the twitter account represented a customer list, and therefore was their property.
This isn't a case of a guy setting up a personal twitter account for personal use, and the company asserting ownership over a personal account. This is a case of a twitter account set up for company/work use, and the guy trying to maintain ownership after he left the company.
There's a big difference between the two. An account set up for someone to tweet for work purposes is clearly a tool that exists for the benefit of the employer. By rights that account does belong to the employer.
Some people who are employed tweet things on their employers benefit from their personal account. Some of the twitter relationships they build will be focused on the work they do for that employer. This is a messy situation because their twitter account will end up being used for both personal and work purposes.
A principle I've always followed is to only use employer-provided tools to do my job. My work is usually software engineering, and I use employer-provided computers to write software for my employer. I do not use personally owned computers to write software for my employer. Likewise any software I write for my own purpose and not meant to be given to my employer, I write that software using personally owned computers. I do my best to not mix the two. It seems to maintain a clear ownership boundary between work and personal creations.
Likewise at times I've had the privilege of blogging for company purposes, on company time. Each time I kept my personal blogging on my own website, and company blogging on the company website. Same reasoning, to maintain a clear ownership boundary.