Email Password Hacking - Password Cracking
This is the method that is always shown in the movies. Someone can pull up the login screen, pull up a little program and then run through all available passwords in a few seconds and find their password. Naturally this isn't how it really works.
This method is called "brute force." It runs through all possible passwords. It's like trying to open a combination lock by going "1-1-1...1-1-2." Note that this can take a really long time unless they have a very powerful network. There are ten numbers and 26 letters that can be used along with a lot of symbols that can be thrown in. Passwords generally have to be 8 characters or more. Ignoring the mess that symbols create, it would take 36^8, or 2,821,109,907,456 attempts to go through all available combinations. So yes, it will take awhile to actually do this unless they're using a few supercomputers, in which case you'd be far below their radar. They would also have to be careful to not have their IP address flagged for a high number of attempts. It's not uncommon for a site to just lock an account down after a few failed attempts in a short period, since it just assumes that a crack attempt is occurring. Again, a botnet can overcome this, but people with such a network usually have more important things to do or lucrative jobs stopping hackers.
There are also programs that just run through the dictionary. They're much quicker but they can fail as long as you throw a number into the email password.
Naturally there are some exploits that come out that allow a quick hack. Sometimes source code is compromised too. Thankfully any good email provider will try to stay on top of these security exploits and close them as quickly as possible. The truth is that email password hacking is usually due to more mundane and non-hacking methods.