Many people argue that success in life is related to being rich and having a successful career [this is taken directly from the title – it is important to paraphrase]. However, in my opinion [this would be better phrased as 'it could be argued that'], there are several other factors that have to be considered, as as I will now explain ['as will now be explained' is more academic].
Primarily, the definition of success can be extremely controversial. There can be as many types of success in life [this is a repeat of the opening phrase used in the introduction] as there are people. For example, the meaning of success for some people living in the countryside might be vastly different from these ['those'] living in the big ['major' would be more academic] cities. In general, people in the countryside thrive for ['thrive on' or 'strive for'] social respect, [no need for a comma here] and family values rather than monetary accounts [this isn't clear – it could be 'monetary gain']. They seem to be happier when they feel respected by their relatives, or their ideas ['opinions' suits better] are considered highly among their community.
Moreover, a considerable portion ['proportion'] of people find their satisfaction in good education. They have eagerness ['an eagerness'] to learn and gain more knowledge. They believe [these setences could be combined – '…knowledge, believing'] that knowledge [use a reference word to avoid repetition – 'this'] is power and a way to lighten their minds and lives. To illustrate, many scientists have devoted their lives in ['to'] research to make a discovery or an invention, and even thought ['though'] these people did ['may'] not have luxurious lives, not many can argue that they were not successful.
Furthermore, in many cases, we judge others ['people are judged' – avoid using we] by their outside appearance; that they are successful because they own, for example, a big ['large' is a little more academic] house, an expensive car, or a good business. But ['However,'] owning these items would not always make them feel successful unless for instant ['instance'], their family life is stable, their health is in good shape, or they really feel satisfied with what they have.
To conclude, I believe that there are many factors that should be taken into account besides wealth and successful career [this is directly from the title] before judging that ['whether'] a person is really successful in his life.
Although certain phrases could have been more academically expressed, this is a well presented response to the task and is laid out in logical paragraphs.
Avoiding the use of the personal pronoun 'I' would make the essay more academic, as well as upgrading some of the vocabulary (e.g. 'big cities' could be expressed as 'larger urban areas').
Linking words could also be improved, especially avoiding beginning a sentence with 'But'.