The time it takes to break a random password is dependent on 3 factors:
The set of characters used to build the password (Eg. lower case only, alphanumeric, etc)
The length of the password.
The speed of the computer breaking the password.
Use the applet below to estimate the maximum time it would take to break a password and determine which factor is most critical in building a strong password.
You can also go to this website to check how secure your password is.