Muslims are required to believe in all previous books sent by God including Torah and Injil (verses 2:2, 2:285). Regarding these books Quran states that the new book sent to Mohammad (PBUH) confirms what is in the hands of the followers of the previous books (i.e. what Christians and Jews had at the time of the prophet which we know is the same as the current books) and clarifies what is disputed among them (e.g. verse 2:41).
It also maintains that parts of the previous books has been altered (though I don't remember any verse that explicitly says this about Injil, it mainly object to what Christians say not to the book). Regarding Jews it states that some Jewish scholars write words from themselves and then claim that it is from God.
The contents of the four gospels are more or less consistent with Islamic views, though some are a bit less so. In particular, the opening part of the gospel according to John, and the parts regarding Jesus's (PBUH) death and resurrection are not consistent with Quran. Also the word son and father should be interpreted the same way as those in Old Testament and should not be held as literal in the way they are interpreted today by most Christians. In other words Jesus (PBUH) is called "son of God" the same way that Israelities and other are referred to as such in the books of Old Testament.
I should add that considering the importance of these beliefs for most Christians today, one can say the Christian reading of these books are heavily inconsistent with Islam and Quran explicitly points out these as false. According to Quran, Jesus was a human born without a father, the analogy for his creation in Quran is the creation of Adam, he was a major prophet but not son of God (there is no such thing according to Quran), he was taken (from Earth/this world) and ascended towards God, he was not put on cross and he didn't die. There are also some other minor points where Quran's narration differs from those of some the gospels.
These does not apply to the other books of the new testament (e.g. writings of the apostles) and the rulings of the Church (e.g. the rulings in 3rd century A.D. about Jesus (PBUH) being God and trinity).
A considerable part of Quran is devoted to speaking with Jews and Christians and in such arguments Quran often refers to the contents of the Torah and Injil to advance its point. Also Quran says that in case Jews/Christians do not accept Islam and remain on their religion they should follow the rulings of their own books. For example, the verse following the one mentioned in SystemDown answer (verse 5:47) says:
وَلْيَحْكُمْ أَهْلُ الْإِنجِيلِ بِمَا أَنزَلَ اللَّهُ فِيهِ ۚ وَمَن لَّمْ يَحْكُم بِمَا أَنزَلَ اللَّهُ فَأُولَٰئِكَ هُمُ الْفَاسِقُونَ
And the followers of Injil must judge based on what is sent in it and whoever does not judge based on what God has sent those are the rebellious.
and continues with (verse 5:48):
وَأَنزَلْنَا إِلَيْكَ الْكِتَابَ بِالْحَقِّ مُصَدِّقًا لِّمَا بَيْنَ يَدَيْهِ مِنَ الْكِتَابِ وَمُهَيْمِنًا عَلَيْهِ ۖ فَاحْكُم بَيْنَهُم بِمَا أَنزَلَ اللَّهُ ۖ وَلَا تَتَّبِعْ أَهْوَاءَهُمْ عَمَّا جَاءَكَ مِنَ الْحَقِّ ۚ لِكُلٍّ جَعَلْنَا مِنكُمْ شِرْعَةً وَمِنْهَاجًا ۚ وَلَوْ شَاءَ اللَّهُ لَجَعَلَكُمْ أُمَّةً وَاحِدَةً وَلَٰكِن لِّيَبْلُوَكُمْ فِي مَا آتَاكُمْ ۖ فَاسْتَبِقُوا الْخَيْرَاتِ ۚ إِلَى اللَّهِ مَرْجِعُكُمْ جَمِيعًا فَيُنَبِّئُكُم بِمَا كُنتُمْ فِيهِ تَخْتَلِفُونَ
And truthfully we sent to you the book, a confirmation to what is between their hands from the book and a guardian on them, thus judge between them based on what God has sent and do not follow their desires while the truth has come to you, for each of you we have put a [set of religious] laws and a light and if God wanted he could make [all of you] one nation but [God wants] to test you about what he has given to you. So hasten towards doing good, towards God is your return, all of you, then he will tell you about what you disputed on.
and (verse 5:49):
وَأَنِ احْكُم بَيْنَهُم بِمَا أَنزَلَ اللَّهُ وَلَا تَتَّبِعْ أَهْوَاءَهُمْ وَاحْذَرْهُمْ أَن يَفْتِنُوكَ عَن بَعْضِ مَا أَنزَلَ اللَّهُ إِلَيْكَ ۖ فَإِن تَوَلَّوْا فَاعْلَمْ أَنَّمَا يُرِيدُ اللَّهُ أَن يُصِيبَهُم بِبَعْضِ ذُنُوبِهِمْ ۗ وَإِنَّ كَثِيرًا مِّنَ النَّاسِ لَفَاسِقُونَ
and judge between them based on what God has sent and do not follow their desires, and be alert of them lest they beguile you from some of what God has sent to you. And if they turn away, be assured that for some of their crime it is God's will to punish them. And truly most people are rebellious.
From these it seems that Quran orders the prophet to rule among Christians based on their own book.
In verses 3:113-115 Quran says:
لَيْسُوا سَوَاءً ۗ مِّنْ أَهْلِ الْكِتَابِ أُمَّةٌ قَائِمَةٌ يَتْلُونَ آيَاتِ اللَّهِ آنَاءَ اللَّيْلِ وَهُمْ يَسْجُدُونَ
Not all of them are alike, of the people of the book are a portion that stay up rehearsing the signs of God all night long, and they prostrate themselves in adoration.
يُؤْمِنُونَ بِاللَّهِ وَالْيَوْمِ الْآخِرِ وَيَأْمُرُونَ بِالْمَعْرُوفِ وَيَنْهَوْنَ عَنِ الْمُنكَرِ وَيُسَارِعُونَ فِي الْخَيْرَاتِ وَأُولَٰئِكَ مِنَ الصَّالِحِينَ
They believe in God and the judgement day; they enjoin what is right, and forbid what is wrong; and they hasten in [doing] good works, they are in the ranks of the righteous.
وَمَا يَفْعَلُوا مِنْ خَيْرٍ فَلَن يُكْفَرُوهُ ۗ وَاللَّهُ عَلِيمٌ بِالْمُتَّقِينَ
Of the good that they do, nothing will be rejected; and God is omniscience about the righteous.
In these verses, "signs" seems to refer the verses of their own books. In addition to the context of these verses which is about the people of the book and not Muslims, the fact that verse 3:114 does not include believing in Quran and the prophet seems to support the fact that these are not the people of the book who have accepted Islam.
Quran's general attitude seems to be that these are good books (even in their current altered versions), Quran confirms what is right in them and points out the parts that they have been altered (at least the most important issues).