There is no law against having multiple Twitter accounts. In fact, for people using Twitter for multiple reasons or even people who are passionate about multiple things, more than one Twitter account is very beneficial.
Behind all of the Twitter chaos, there is a strategy. People who excel at Twitter are people who understand niches and have interesting things to say about them.
Here are specific cases which should have separate Twitter accounts:
Personal - Your personal Twitter account should be all about you: what you're doing, any interesting links you might find, and your conversations with your friends. It might even be your attempt at conversing with celebrities or people of interest. This Twitter should represent you and highlight your personality. Do not simply tweet that you're going to the grocery store or that you're going to the gym--that's boring. Tweet interesting things--or if you want to tweet about what you're doing, add a special twist. Everyone is unique in their own way and Twitter is a great way to show your personality.
Business - A company's Twitter account should be strictly professional and represent the brand of that specific company. Companies have succeeded at even having multiple Twitter accounts: one for news, one for customer service, one for interesting facts, etc. You can have as many as you want as long as you keep up with them and interact with the community. If you have the manpower and time, more power to you and your company. You definitely want a separate Twitter account for business and for pleasure because you don't want to tweet about the wrong things to the wrong audience. You don't want to talk about how much food you ate or how insane your Saturday night was to prospective clients.
Interests - If you are an avid San Diego Chargers fan and know everything there is to know about that team, then create a username and tweet about it. Make sure to put something about this specific interest in the username and the description or else people who search for this interest won't be able to find you. You want to make yourself as accessible as possible to prospective followers. With Twitter accounts like these, if you gain thousands of followers, you might even be able to sell it. Have as many of these as you think you can manage.
What about followers? Isn't it hard to gain a significant number of followers for each user account? Nowadays, people have many Twitter accounts. If you have Twitter accounts that appeal to different niches, you will get more targeted followers that are interested in 90% of what you are tweeting about, as opposed to trying to put all of your followers on the same feed. You will actually have a greater follower turn out if you specialize your interests and cater them to the following audience you would like to have.
Multiple Twitter accounts are easy to manage now because of apps like HootSuite and TweetDeck. You can select which one of your profiles you would like to Tweet to from these platforms, and no one will know that the person behind these accounts is the same person unless you want them to.