The time of 8 character passwords is over. A 12-16 character long password is fairly standard these days, but more and more sites are allowing even longer passwords than that. Take Weebly.com for example which, allows up to 160 characters.
Most web browsers these days have a password manager which, takes away the pain of remembering long passwords, but that still leaves the difficulty of coming up with them in the first place. There are websites which will do it for you, but personally I prefer not to rely on 3rd parties.
Below is a simple Bash script I use for generating passwords. It's not pretty, but it works. You'll need to change '10000' to the password length you need. The password will be outputted as plain-text to a file called "password" in the present working directory (eg: your home directory). This script depends on: head, base64, sed, and bash. It also uses the urandom block device.
head -c "$length" /dev/urandom | base64 -w 0 | sed 's/=//g' | sed 's///#/g' | sed 's/+/$/g' | head -c "$length" > password