Is it advisable to apply to graduate programs after the deadline has passed?

You could try contacting the graduate administrator for programs you wanted to apply to, and ask them if it is too late to apply. I would consider doing this before I'd start throwing hundreds of dollars in applications to programs who wouldn't consider my app at all, anyway. However, most programs I've dealt with have online applications that are all marked as closed and won't allow any new applications, even if you wanted to apply, if it is after the selection date.

I don't personally know anyone who has tried this, but I suppose the most it will cost you is a polite email.

In all honesty though, I really don't expect anything other than a "you are welcomed to apply next year" response. A few graduate programs with deadlines in December have already made their decisions, some have contacted students for interviews, and some haven't started reviewing files (but admissions has still been processing their files, ensuring everything is attached, etc). Those that haven't started may still not allow any new applications.

You can ask, but most likely you will need to consider alternative plans, such as looking at programs that have spring admissions, dates that haven't passed, or just waiting until fall of 2017 to apply for fall of 2018. Good luck, regardless!

You are less likely to get into a program the closer to a deadline the application is, because most schools have rolling admissions programs and will have already started accepting people. Applying late can give off the false impression that the application is an afterthought, and with so little time, you will also be rushing letter writers, trying to get transcripts, and more likely to make an error that cannot be corrected in time.

GRE scores are good for five years. You would likely be better off finding an internship or work experience than applying this late in the cycle.