For instance, you'd want to write: "Earned Best in Class award for increasing sales 16% over previous quarter." instead of "Earned the Best in Class award for increasing sales 16% over the previous quarter."
As we move (slowly) towards a recruiting and job search environment that relies more and more on candidates' Ideas and the real value they bring to the table, resume content is shifting. With that, there's a bit more flexibility, but you still want to avoid overusing articles.
You'll find that great resumes will have more articles than they used to. That's not a big deal. Sometimes articles make something "read" more effectively or they anchor an especially complex bullet.
This is also a good time to speak to another convention - implied first person - that is also the norm. Never use "I" or "my" on a resume but always write from the first person. These pronouns are always implied. No exceptions. Some people make the mistake of taking a third person voice on their resumes. This is a big no-no and sends the wrong message.
These can be especially tricky concepts to understand, so be sure to send off an e-mail if you need clarification.
Also, be sure to have a look at Tandem's current promotion.