Four situations (out of many more :) when you shouldn't use articles:
1. Before abstract nouns used in a general sense.
ex. Happiness is hard to find, Crime is up this year.
2. With many cities or countries.
ex. I live in London, She is from France.
3. With names of sports.
ex. I play tennis, He played volleyball.
4. In front of company names.
ex. She works at Walmart, He got fired from Sony.
This can be a fairly difficult topic for ESL students, but there are many sites that can clarify it for you :) If you'd like more information about articles (definite and indefinite) and their usage (or in this case non-usage), check out the Use and Non-Use of Articles (Purdue University) page.