There are a lot of simple habits that you can develop that make it really hard to get phished.
1. Stay Calm - This may sound a little patronizing, but it's the best advice that I can give. In a number of the phishing scams that I know about, the victim usually panics and makes a mistake. Stories of phishing victims have this as a recurring element. This even happened to a relative of mine once too. She freaked out upon hearing that her eBay account might be closed down, so she gave a bunch of her information to a scammer (She figured it out in time and cancelled her credit cards, but she's a lucky case).
The people who send phishing emails depend on you not examining their email or their claims. That's why they always have a strong call to action to try to make you act without thinking. Overcoming this will usually be enough to overcome their scams.
2. Never Share Your Information - I'll cover some specifics in a little bit, but this simple step is another great habit. You should always be very careful about giving out your information. Only give it out to websites and individuals that you completely trust. When you do this, also look in the bottom right corner of your browser for a locked padlock. If your trusted website isn't encrypted properly, then it's possible that someone can snag your information in transit. Also check the address bar to make sure that you're really on the right website. Several scammers use websites that look like official pages, but in reality are fake versions of the website on a different domain name.
3. Examine Your Emails - This is another simple one. Just check the suspected phishing email for the usual signs. Do they just call you a "member?" Most banks and organizations will have your name or a nickname and it will be automatically inserted into their form letters. You can easily avoid phishing scams by just checking to see the header to see whether they actually know anything about you. Also check to see whether the logo and headers are lined up right. Most phishing emails are pretty poorly made. Finally, since many phishing scams are based out of countries where English is not spoken as a primary language, there are often spelling errors. Check for those.
4. Think - This is close to number one, but the point is the same. Why do they need this information? If you're already signed up, then why don't they have it? Your bank or credit card company doesn't usually need your number. They should already have it. Steam, Xbox Live and World of Warcraft do not need your login information. They could look it up quickly.