I want to marry a girl but to my family disapproved it. Do I have the right in Islam to disobey the wishes of my family and marry her?
Actually a man a priori doesn't need his family permission for marrying, or for doing anything else, but the problem rise when his father or father of father (and not the others, including, mother, sisters or brothers, grandparents of the mother side, mother of father and etc.) ban him from doing something or force him to do another thing: obeying father is obligatory and obeying the father of father is more obligatory (since obeying him is obligatory even for his father).
In regard with mother and the other grandparents we have only ordered to keep them satisfied. If they disagree the man can talk with them mildly, make them happy, promises some good promises and etc. all to change their mind, to be happy with what the man is to do. But about the father the problem persists, obeying him is a must.
Once I was in a similar situation (though not exactly the same) and thus to some extent know how you may feel. But have this piece of caution from me, Allah never put what is good for you in the way He has banned for you. If you insist on what you like Allah may give it to you but then one day you will be regretful of the choice you make today:
ذَٰلِكَ بِأَنَّ اللَّـهَ لَمْ يَكُ مُغَيِّرًا نِّعْمَةً أَنْعَمَهَا عَلَىٰ قَوْمٍ حَتَّىٰ يُغَيِّرُوا مَا بِأَنفُسِهِمْ ۙ وَأَنَّ اللَّـهَ سَمِيعٌ عَلِيمٌ
"Because Allah will never change the grace which He hath bestowed on a people until they change what is in their (own) souls: and verily Allah is He Who heareth and knoweth (all things)." [Al-Anfal,53]
... وَعَسَىٰ أَن تَكْرَهُوا شَيْئًا وَهُوَ خَيْرٌ لَّكُمْ ۖ وَعَسَىٰ أَن تُحِبُّوا شَيْئًا وَهُوَ شَرٌّ لَّكُمْ ۗ وَاللَّـهُ يَعْلَمُ وَأَنتُمْ لَا تَعْلَمُونَ
... But it is possible that ye dislike a thing which is good for you, and that ye love a thing which is bad for you. But Allah knoweth, and ye know not. [Al-Baqarah,216]
Insisting on what we think is good for us after we understood it is prohibited by Allah is called ignorance in Quran:
وَنَادَىٰ نُوحٌ رَّبَّهُ فَقَالَ رَبِّ إِنَّ ابْنِي مِنْ أَهْلِي وَإِنَّ وَعْدَكَ الْحَقُّ وَأَنتَ أَحْكَمُ الْحَاكِمِينَ / قَالَ يَا نُوحُ إِنَّهُ لَيْسَ مِنْ أَهْلِكَ ۖ إِنَّهُ عَمَلٌ غَيْرُ صَالِحٍ ۖ فَلَا تَسْأَلْنِ مَا لَيْسَ لَكَ بِهِ عِلْمٌ ۖ إِنِّي أَعِظُكَ أَن تَكُونَ مِنَ الْجَاهِلِينَ
And Noah called upon his Lord, and said: "O my Lord! Surely my son is of my family! And Thy promise is true, and Thou art the justest of Judges!" / He said: "O Noah! He is not of thy family: For his conduct is unrighteous. So ask not of Me that of which thou hast no knowledge! I give thee counsel, lest thou act like the ignorant!" [Hud,45,46]
Some youth were asking such questions from a scholar and he humorously answered something like this "in older days when someone was afraid of such things he was marrying in stealth and when he has got two children was coming to his father's home with his family in open, showing his father his wife and children". This was not serious though and is not especially in this era, but at least it shows a way how youths are better to manage their relationships with their fathers. For example someone is going to swim with his friend; if he asks his father "may I go with my friends out to swim?" his father may simply say "don't go you may catch cold" and it would be Haram for him to go to swim that they, but if the guy instead says to his father "Dad I am going to swim" his father may say "be careful not to catch cold". This is an art, two sayings that have the same message can work completely differently in application. Seemingly, especially when you are to introduce your choice to your father you should be extremely careful for him not to say "no". About the rest of family the problem is not always unresolvable.
This is not a very easy doing, Hope that Allah would let me and all of us to yield in front of Allah in all the respects.
The view that "it is obligatory to obey your farther (and grandfather)" expressed in owari's answer is a very common view (probably even the dominant Muslim view on the issue). However, despite being a very common view I found it contradictory to Quran (as I understand it). Let me explain.
Based on my understanding of Quran, you don't need to obey your parents. What God asks in Quran regarding parents is "ihsan" towards them not obedience. Not only there isn't even a single verse in Quran that asks for obedience towards parents, but also there are many verses that strongly warn against blindly following others, including parents. It is not just following wishes of self (what Quran refers to by "الْهَوَىٰ") that leads one to go astray. Blindly following fathers (what Quranic refers to by "آبَاء") also leads one to go astray. There are many strong warning verses regarding this, and it is one of the strongest repeated themes in Quran, e.g. see verses 2:170, 5:104, 7:28, 7:70, 10:78, 31:21, 43:23, ... In fact all except one occurrence of "following fathers" in Quran are negative. (The exception is the verse 12:28 where Yusof (PBUH) says he follows the religion of his fathers Ibrahim, Is'haq, and Yaqub (PBUT).) There is also a very general and explicit verse which asks one not to follow what one does not have knowledge about:
وَلَا تَقْفُ مَا لَيْسَ لَكَ بِهِ عِلْمٌ إِنَّ السَّمْعَ وَالْبَصَرَ وَالْفُؤَادَ كُلُّ أُولَٰئِكَ كَانَ عَنْهُ مَسْئُولًا
And do not pursue that of which you have no knowledge, indeed, the hearing, the sight, and the heart, all of those [one] will be questioned of.
So why is the view that one should follow one's fathers is so common? The answer is that this is how tradition works. It is hard to sustain a tradition when all things are open to question and the wishes of fathers is not required to be followed. It is common for traditions (including the Islamic traditions) to require obedience from fathers. In traditional societies typically it is fathers and grandfathers who play the role of the maintainer of the traditions. To do this they need authority which the view expressed in owari's answer gives them. But as I have explained the view is not supported by Quran and in fact is contrary to Quran (as I understand it). According to Quran blinding following fathers (tradition) is one of the two main causes of going astray and is strongly forbidden and condemned.
As owari has written it is also common view that following one's grandfather is even more important than following one's father. There is absolutely nothing like that in Quran. Grandfather is just a relative, nothing more. They are not mentioned in the verses that asks one to be good towards parents (verses always refer to both parents, not just father). But grandfathers are mentioned nowhere in similar terms, and have no special place in Quran other than being a relative.
After the general rule regarding not following fathers blindly, I should add that there are very strong verses that ask one to be good and kind (the Quranic word is "ihsan" which is the limit of being good) towards parents:
وَقَضَىٰ رَبُّكَ أَلَّا تَعْبُدُوا إِلَّا إِيَّاهُ وَبِالْوَالِدَيْنِ إِحْسَانًا ۚ إِمَّا يَبْلُغَنَّ عِندَكَ الْكِبَرَ أَحَدُهُمَا أَوْ كِلَاهُمَا فَلَا تَقُل لَّهُمَا أُفٍّ وَلَا تَنْهَرْهُمَا وَقُل لَّهُمَا قَوْلًا كَرِيمًا
وَاخْفِضْ لَهُمَا جَنَاحَ الذُّلِّ مِنَ الرَّحْمَةِ وَقُل رَّبِّ ارْحَمْهُمَا كَمَا رَبَّيَانِي صَغِيرًا
And your Lord decreed that you not serve but Him, and towards parents goodness. Whether one or both of them reach old age [while] with you, say not to them "uff" (a word of contempt), nor repel them, but address them in noble terms.
And lower to them the wing of humility out of kindness, and say: "My Lord! bestow on them thy Mercy even as they cherished me in childhood."
The verse implies that you should serve only God, not your parents. What you are asked regarding them is not obedience but extreme goodness and kindness. At the same time, by stating this next to the decree that one should only serve God, it shows the importance of being good and kind towards parents.
If you think what you do is in accordance with God's will, you don't need to obey your father's (or grandfather's) wish in addition to that. But you should try your best to be good and kind towards your parents. Keep in mind that parents typically look for the best for their children, and based on their experience may see problems that you don't. Also remember that often strong feelings make people blind towards reality and what is God's will, so be careful.