Here is a wikipedia list of a bunch of different email scams that have popped up.
Some common ones I've encountered are emails that appear to be from facebook or other known websites where you have a login and password, and request you to use their link to input your email and password to log in. Once you've done this, you've given them your information for them to hack your account and send spam to all your friends and family. Best practice is to never open these types of emails unless you know it is in fact from the website. However, if you do believe it is from the real source, and want to follow a link within an email, make sure to check the web address, and make sure it one you would normally log in to.
Other common scams have to do with money, jobs, bank accounts, dating sites or deals.
As my mother always told me, if it sounds too good to be true, it probably is.