Corrections in red.  Stylistic suggestions in blue.

FCE ESSAY: Because Cars are So Convenient, Public Transportation [1] Has No Future [2]

In today´s world, due to the fact the great comfortability of cars, public transportation is likely to disappear.

Firstly, is it true that cars are a faster way of transportation.  However, [3] there are many people who can't afford a car.
Furthermore, a car is one of the most popular means of transportion, not only because of its speed, but also because public transportion fares increase each year. From my point of view, many people use cars owing/due to the awful quality of some buses, trains…

We should also consider the fact that nowadays life is so busy that we can´t waste our time taking public transportation.  However, cars can cause some problems like traffic jams and accidents that could be avoided using public transportion. 

To conclude, it seems to me that it is fine to use cars sometimes, but if the quality of public transportation were [subjunctive!] better, the amount of pollution and accidents would decrease.

[1]  For human beings, "transportation" sounds better. For cargo, "transport" is often used.

[2]  Capitalize the "important" words in a title, and the first and last words.  "Important" words do not include prepositions, articles, and the conjugated forms of the verb "to be".

[3]  "However" indicates the <em>conflict</em> between the preceding sentence, and the sentence beginning with "However".