Some very fine tutorials have been written, over the years. Michael Doob's splendid 'Gentle Introduction' to Plain TeX (available on CTAN) has been stable for a very long time. Another contender in the same game is from one D. R. Wilkins, available on the web at http://www.ntg.nl/doc/wilkins/pllong.pdf
Tobias Oetiker's '(Not so) Short Introduction to LaTeX2e', is regularly updated, as people suggest better ways of explaining things, etc. The introduction is available on CTAN, together with versions in the some of the many languages it has been translated into.
Harvey Greenberg's 'Simplified Introduction to LaTeX' was written for a lecture course, and is also available on CTAN (in PostScript only, unfortunately).
Edith Hodgen's LaTeX, a Braindump starts you from the ground up - giving a basic tutorial in the use of Linux to get you going (rather a large file...). Its parent site, David Friggens' documentation page is a useful collection of links in itself.
Peter Flynn's "Beginner's LaTeX" (which also started as course material) is a pleasing read. A complete copy may be found on CTAN, but it may also be browsed over the web (http://www.tex.ac.uk/tex-archive/info/beginlatex/html/).
TUG India is developing a series of online LaTeX tutorials which can be strongly recommended: select single chapters at a time from http://www.tug.org.in/tutorials.html - the set comprises two parts, "Text" and "Graphics", so far.
Andy Roberts' introductory material is a pleasing short introduction to the use of (La)TeX; some of the slides for actual tutorials are to be found on the page, as well.
Another item, not quite FAQ, not quite tutorial, is Herbert Voss's excellent LaTeX tips and tricks.
An interesting (and practical) tutorial about what not to do is l2tabu, or "A list of sins of LaTeX2e users" by Mark Trettin, translated into English by Jürgen Fenn. The tutorial is available from CTAN as a PDF file (though the source is also available).
The AMS publishes a "Short Math Guide for LaTeX", which is available (in several formats) via http://www.ams.org/tex/short-math-guide.html
Herbert Voss is developing a parallel document, that is also very useful; it's part of his "tips and tricks" mentioned above and is also available on CTAN.
Keith Reckdahl's "Using Imported Graphics in LaTeX2e" is an excellent introduction to graphics use, though it's slightly dated in not discussing anything other than the dvips route. Available on CTAN, but again without sources.
An invaluable step-by-step setup guide for establishing a "work flow" through your (La)TeX system, so that output appears at the correct size and position on standard-sized paper, and that the print quality is satisfactory, is Mike Shell's testflow. The tutorial consists of a large plain text document, and there is a supporting LaTeX file together with correct output, both in PostScript and PDF, for each of A4 and "letter" paper sizes. The complete kit is available on CTAN (distributed with the author's macros for papers submitted for IEEE publications).
For Plain TeX commands a rather nice quick reference booklet, by John W. Shipman, is available.
Special-purpose tutorials are always useful, and an example is set by Haruhiko Okumura's page on typesetting Japanese with Omega (the parent page is in Japanese, so out of the scope of this FAQ).
Some university departments make their local documentation available on the web. Most straightforwardly, there's the simple translation of existing documentation into HTML, for example the INFO documentation of the (La)TeX installation, of which a sample is the LaTeX documentation available at http://www.tac.dk/cgi-bin/info2www?(latex)
More ambitiously, some university departments have enthusiastic documenters who make public record of their (La)TeX support. For example, Tim Love (of Cambridge University Engineering Department) maintains his deparment's pages at http://www-h.eng.cam.ac.uk/help/tpl/textprocessing/, and Mimi Burbank (of the School of Computer Science & Information Technology at the University of Florida) manages her department's at http://www.csit.fsu.edu/~mimi/tex/ - both sets are fine examples of good practice.
People have long argued for (La)TeX books to be made available on the web, and Victor Eijkhout's excellent "TeX by Topic" (previously published by Addison-Wesley, but long out of print) was offered in this way at Christmas 2001. The book is currently available at http://www.eijkhout.net/tbt/; it's not a beginner's tutorial but it's a fine reference (contributions are invited, and the book is well worth the suggested contribution).
Addison-Wesley have also released the copyright of "TeX for the Impatient" by Paul W. Abrahams, Karl Berry and Kathryn A. Hargreaves, another book whose unavailability many have lamented. The authors have re-released the book under the GNU general documentation licence, and it is available from CTAN.
Norm Walsh's "Making TeX Work" is also available (free) on the Web, at http://makingtexwork.sourceforge.net/mtw/; the sources of the Web page are on CTAN.
The book was an excellent resource in its day, but is now somewhat dated; nevertheless, it still has its uses, and is a welcome addition to the list of on-line resources. A project to update it is believed to be under way.
Jim Hefferon maintains a web page "Managing a one-person TeX system" which provides a useful introduction to those who find they need to manage a TeX system on a personal machine. It covers much of the matters discussed in answers such as "Where to put new files", and thereby covers the gap left by the (possibly temporary) lack of "Making TeX work".
There's also (at least one) typographic style tutorial available on the Web, the excellent "Guidelines for Typography in NBCS". In fact, its parent page is also worth a read: among other things, it provides copies of the "guidelines" document in a wide variety of primary fonts, for comparison purposes. The author is careful to explain that he has no ambition to supplant such excellent books as Bringhurst's, but the document (though it does contain its Rutgers-local matter) is a fine introduction to the issues of producing readable documents.
This question on the Web: http://www.tex.ac.uk/cgi-bin/texfaq2html?label=tutorials