Should I focus on a single extra curricular activity?

What if I'm passionate about too many things? That's always been my problem-- I run a club with ~30 members at the local middle school teaching students to write, but I also love math and science and did research at a very well-known university last summer and will be presenting at a conference in December. I also love a thousand other things--international affairs, performing arts, etc.

How do I look strong and focused on a college application if I'm passionate about everything? Is it okay to have a wide array of interests instead of one activity for many years?

You've done impressive things despite the wide-ranging nature of your interests, so I don't think you should worry about your application looking too eclectic and unfocused. The main reason why students are told not to pursue too many different activities in high school is because it can lead to a slew of unremarkable extracurricular accomplishments rather than one or two really great ones.

Your club and your research experience are not just dime-a-dozen activities - both are great examples of unique achievements that will add value to your application. There's no such thing as being passionate about too many subjects if you're still able to make your accomplishments stand out in certain areas. Just emphasize your largest successes over minor extracurricular activities on your application. Your love of learning and passion for a variety of different subjects could even make a great essay topic!