Does emergency contraception exist?

Yes. It is most useful and effective the sooner it is taken to unprotected intercourse.
Yes. There are several brands now. Plan b being the most popular. In most states it is available over the counter for those over 18.
Yes. Plan b one-step is over the counter and is levonorgesterol. It is most effective if taken right away. Ella (ulipristal acetate) requires a prescription, contains ulipristal, and may be a bit more effective after a few days. The copper containing iud, paraguard is also a highly effective emergency contraceptive that is good for 10 years.
Some ECP options. include Ella, Aftera, After pills, Athenitia Next, EContra Ez, Fallback Solo, My Way, Next Choice One Dose, Opcicon One- Step, Option 2, Take Action & Plan B One-Step. Additionally, a number of combined progestin/ estrogen pills can be used in higher doses as emergency contraception.