Google is a programmer's best resource. No one remembers every API ever made, memorization isn't what makes a good programmer, being able to look something up and figure out how to use it correctly is (along with a bunch of other stuff).

If there is one thing I learned in college to feel like a programmer finally it was learning to use google effectively. I feel like with google and enough time I could pretty much program anything asked for me. That's how you know you are a programmer.

EDIT: I didn't feel like a programmer until I started my own project in my free time. A lot of programmers starting out feel that they know how to do for loops, if statements, even complex algorithms, but they still feel like they don't know how to 'make' anything that they think would be cool or useful. That's how I felt until I decided to make a server plugin for Minecraft, started with the basics and built up from there using the bukkit APIs. Before I knew it I had a complex plugin that did a lot of cool things and the people on my server really enjoyed. Eventually I even released it to the public. I must say when I look back, the plugin was horribly written (and since now has been rewritten in a better way by me and other programmers who now joined me with the project). But I learned so much from the experience, I learned how to use APIs to make something of real use to people, and learned how to structure my code in ways that make more sense, learned to use version control (github), I learned how to apply all the concepts I learned in school to a real world problem.