Let me explain my situation a little bit, then I will try to make it more general for others to benefit.
I am graduating in a month and getting my bachelor degree in computer science. I did apply to graduate programs of US universities, and it did not end up as I expected. Right now, I am still looking for chances, graduate programs, to get in. I guess all the programs in US made their decisions already, and this is true for most of EU universities. But, still I want to check if I am missing anything.
More generally, consider an international student who wants to apply for graduate programs of computer science in EU/US. It is mid of May. Does this student still have chances to get in a graduate program with scholarship?
At my university (Bath), prestigious university scholarships are awarded through a competition that has its first rounds of evaluations in January, so we recommend submitting December of the year before. However, in the UK and Europe generally much research is funded by grants from research councils and industry which may be awarded at any time. These studentships are on particular topics and will be advertised on relevant mailing lists and sites like http://jobs.ac.uk. In addition, often multiple universities offer the same top students studentships, so occasionally funding gets returned and reoffered to a new applicant.
Application times for American academic positions (both faculty and postgraduate) seem to be more structured, at least in my experience. At MIT they said they had at least 120-150 fully-qualified applicants for the 30 slots they had the year I was lucky enough to get in (note: this means getting rejected does NOT necessarily mean you weren't good enough to get in!) So I don't think there is any chance they would look at someone who missed their application deadline if they applied late. But I could be wrong, and certainly it might be different at smaller universities.
In general though I'd recommend spending the time between now & the next deadline making yourself a better candidate, e.g. by publishing, working in a lab, or helping out with a conference or even just getting a job. Even if you put in another application this year, this is still good advice in case you reapply for next year.