"I work at a company." - the speaker might be relating the location of the company he's / she's working with. "I work for a company." - here, the speaker is suggesting that he/she is a part (employee) of the company. the statements however are gramatically correct although, most of the time, you would likely hear the specific company name they are working with: "I work FOR McDonald's (for instance)." or, unspecifically, "I work FOR a well known car manufacturing company." :)