You may have noticed that not all industries recruit and advertise their internship (and job) opportunities at the same times. Many large financial, accounting, and engineering companies do their hiring in the fall semesters, while government tends to hire in early winter, and arts/media in the spring. Other industries fall throughout the year as well.
I encourage you to do some research on your industry to see when you should be anticipating being busy with applications. Even if you are interested in the non-profit/public service world, for example, which typically hires in mid-spring, start researching the organizations now and get an idea of those you are interested in and if possible, make some networking contacts within them now. The Vault and B-Link are great places to get started.
To find out some of the organizations that do have early deadlines for their internships, here is a great site to check out.