Any type of company can apply for an H-1B visa. The position available must meet the requirements of a "specialty occupation" or require at least a college degree. Very small companies of just a couple people are also eligible to apply for an H-1B visa. However, the Department of Homeland Security tends to scrutinize their applications very carefully. That being said a legitimate, well documented petition still has a good chance of approval.
Unfortunately, there are no more H-1B visas available until October 2010 as the cap was reached a couple of weeks ago. One may petition for these visas as early as April 1st. If you know you want to apply for an H-1B visa I would advise submitting your petition so it arrives on April 1st, because in 2007 and 2008 the cap of 65,000 was reached on the very first day USCIS accepted applications.