The following Hadith states that we should fight people (which I presume refers to disbelievers):
I have been directed to fight against these people until they testify to the oneness of God and to the prophethood of Muhammad, establish the prayer and pay zakāh. (Muslim,No:22)
So are we required to kill all disbelievers?
This inference is not correct. As explained by Ghamidi, people who deliberately reject the Messengers of God are punished in this world for this denial. While the polytheists among them are put to death the monotheists among them are subjugated into a life of submission.
This Hadith actually refers to the punishment that would be meted out to the polytheists of Arabia if they refuse to accept faith. In the usage of the Qur'an these are called the mushrikūn. Consequently, another text of this Hadith specifically mentions them by name:
عَنْ أَنَسِ بْنِ مَالِكٍ عَنْ النَّبِيِّ صَلَّى اللَّهُ عَلَيْهِ وَسَلَّمَ قَالَ أُمِرْتُ أَنْ أُقَاتِلَ الْمُشْرِكِينَ حَتَّى يَشْهَدُوا أَنْ لَا إِلَهَ إِلَّا اللَّهُ وَأَنَّ مُحَمَّدًا عَبْدُهُ وَرَسُولُهُ فَإِذَا شَهِدُوا أَنْ لَا إِلَهَ إِلَّا اللَّهُ وَأَنَّ مُحَمَّدًا عَبْدُهُ وَرَسُولُهُ وَصَلَّوْا صَلَاتَنَا وَاسْتَقْبَلُوا قِبْلَتَنَا وَأَكَلُوا ذَبَائِحَنَا فَقَدْ حَرُمَتْ عَلَيْنَا دِمَاؤُهُمْ وَأَمْوَالُهُمْ إِلَّا بِحَقِّهَا
Anas Ibn Mālik reports from the Prophet: "I have been directed to fight against these Idolaters until they testify to the oneness of God and to the fact that Muhammad is his servant and messenger. If they testify to the oneness of God and to the fact that Muhammad is his servant and prophet, establish our prayer and face our qiblah [while praying], and eat our slaughtered animals, their life and wealth we shall hold sacred except if they commit some violation." (Nasā'ī: No: 3966)