It goes without saying that you must have an email address on your resume, and make sure it's professional. Avoid using email addresses that leave a poor impression, and also, if possible, avoid using outdated addresses like Hotmail (now Outlook) that could make you seem behind-the-times. The best choice is something simple like your name. Make sure to check it daily if you're job searching - and always respond within 24 hours.
Personally, I recommend listing just one phone number, not two. Forcing the recruiter to make a decision about which number to call is unnecessary, and it just takes up space. (Having said that, if including two phone numbers is the worst mistake you make on your resume, you're in great shape!) Make sure you have voice mail on that number though - you don't want to miss messages - and always reply within 24 hours.
City - State/Province - Zip/Postal Code
You don't need to include your street address if you're concerned about privacy, but at a minimum you should include your city, state or province, and zip or postal code. I was told by a few recruiters in the past that without your zip/postal code, they can't enter you properly in their database and you may not be found in a database search. Leaving off your street address will help protect your privacy, if that's a concern, but be sure to add the rest.
More and more often, recruiters expect to see a link to your LinkedIn profile on your resume. Sure they can search for you but that's not always easy, especially if you have a common name (like me). Make it easy for them. Create a customized URL for your profile (ie. something like linkedin.com/in/michaelgordonhoward) and include it on your resume and, perhaps, in your email signature. After all, you want to connect with them, right? Feel free to include links to your website and other social media platforms as well, IF you use them for professional purposes.
Obviously you need to include your name at the top of your resume. Make sure it's presented the same way on your resume as your LinkedIn profile, so there's no mistaking that you're one and the same person - so if it's Bob Anderson on your profile, make sure it's not Robert J. Anderson on your resume.
Happy job searching!