Although it may difficult to cite all the sects, what are some major Christian sects that promote "faith healing"?
The concept of "faith healing" is pretty broad and you would need to supply your own definition if you want a very specific answer. Lacking that, here is the general lay of the land.
Most Christian traditions actually believe (have faith) that God can and even does heal people. However I doubt this is what you are referring to. Where most denominations back off is when it comes to the recipient being able to demand (in faith?) to be healed and the result is seen as reflecting on the amount of faith rather than strictly God's sovereign will to say yes or no.
Of the latter kind of faith healing, it is most prevalent among Pentecostal and extreme Charismatic groups. It is given varying degrees of importance from a sometimes mentioned subject to a key item used as primary evidence of belief and even for evangelism.
A few less common groups with less direct ties to Christianity such as the Christian Scientist movement also promote this, although their implementation often varies from the kind of thing you see trumpeted on questionable TV channels.
It does sometimes pop up in other circles, even Catholic ones, but is generally not well received by other traditions. Again, other traditions may believe that God can and does grant healing and our faith plays a role in that, but the kind of belief and practice that probably comes to mind from watching TV evangelists is mostly the domain of Pentecostal movements.
The Christian Science Journal records the healings and spiritual insights of those who faithfully practice Christian Science. Individuals share how an ever-developing understanding of God has healed, enlightened, and blessed them, expanding their spirituality and ability to heal others. Below are a few sample articles.
The Journal also includes a worldwide directory of Christian Science practitioners, teachers, and Christian Science nurses available to anyone interested in spiritual healing, as well as a listing of all Christian Science churches and societies throughout the world. The directory is here as well as in the right column of this page.