Bias by which we tend to accept vague descriptions of ourselves There's an effective strategy employed by horoscopes and "psychics" where they say vague statements like "You like being with friends but you value your time alone"; statements that basically "cover their bases" in multiple extremes and thus apply to just about anyone.

As a typical example in high school our Psychology teacher gave us a "handwriting evaluation" which gave our "personality types" based on our handwriting; the results were just random statements. Everyone got the same statements but most of the class claimed their results were accurate.

What is the name of these types of statements or the bias by which people tend to believe them?
This is referred to as The Forer Effect after Bertram Forer. 
Wikipedia describes it accurately:


  The Forer effect (also called the Barnum Effect after P.T. Barnum's observation that "we've got something for everyone") is the observation that individuals will give high accuracy ratings to descriptions of their personality that supposedly are tailored specifically for them, but are in fact vague and general enough to apply to a wide range of people. This effect can provide a partial explanation for the widespread acceptance of some beliefs and practices, such as astrology, fortune telling, and some types of personality tests.


Forer gave the results of a "personality test" to a group of his students composed of random vague statements compiled from horoscopes. Students were asked to rate it's accuracy on a scale from 0 to 5, and the mean score was 4.26.

Forer discussed these findings and the "experiment" in his article The fallacy of personal validation: a classroom demonstration of gullibility.