These can not really be classified as tests as there are no right or wrong answers. They may be termed personality questionnaires. They usually consist of various statements and you are asked to indicate which statement best reflects your personality. You may well feel that you have been asked the same question several times, just phrased slightly differently. This is normal, it is to gauge consistency in your responses.
The employer will be looking to see if you have the right type of personality to fit into their organisation. They will try to examine your attitude towards change, your flexibility, how you feel about working as part of a team and if you demonstrate initiative. Some personality tests may have a time limit, others will not. Time limits are usually only introduced to force you to answer quickly and not to spend time trying to analyse what the questioner wants and therefore providing a more honest answer.