With so many types of harassment and discrimination out there, I think that several are common, but maybe a few are more common than others. The common types that I see come up most include:
Sexual Harassment - This is probably one of the most common forms of harassment that is talked about. Without proper employee and management training, the employer is setting him or herself up for complaints in this area from his or her employees. Employees tend to make sexual jokes, especially if they don't think anyone else can hear the conversation. There are also people who don't know when to accept someone telling them no when asked out. While I don't think that this form of harassment will ever go away, an employer can take steps to reduce liability by informing employees as to what sexual harassment is, what can be construed as sexual harassment, what the company policy is, and they hold employees accountable for their actions. This is probably also one of the easiest to prove in court.
Disability Discrimination - This one, unfortunately, is still prevalent in society - even with the laws. Employers may think that hiring a disabled individual is just not worth the changes they would need to make to the place of employment to accommodate the individual. My company is great with how they hire individuals who are qualified for the position and they don't base their determination on whether or not the individual has a disability.
Age Discrimination - This one is still common because employers tend to look for individuals in certain age groups to fill specific roles in their business (for some roles). For example, an individual who looks or acts very young (18 - 25) may not be right for a director or executive role, even if that individual has the experience to back him or her. While I have not yet met a fully 'mature' director, I also haven't met one that is under 40 (or so). On the flip side, a sales company most likely would be
looking for someone in the 18 - 25 years old range for frontline sales because someone who is younger will likely have more energy. Now, these of course are discriminatory, but this does happen. Employers, in some cases, do rate applicants based on their age rather than their qualifications.
Race Discrimination - This one, unfortunately, is still an issue in today's society. Of course, not every employer bases his or her hiring determination on an individual's race, but it does happen. For example, I have a friend who is African American and he was flat out told by an interviewer that they would not hire him because they didn't feel he would 'fit in' with the rest of their employees. This is completely illegal and unethical. Yes, my friend is suing them right now.
The bottom line is this: be careful what you say and how you act even if you think they aren't looking. Just don't even let it come out of your mouth or be written down anywhere. Not discriminating or harassing anyone is your safest bet to not be sued for discrimination.