A pleasing little document, “Getting something out of LaTeX” is designed to give a feel of LaTeX to someone who's never used it at all. It's not a tutorial, merely helps the user to decide whether to go on to a tutorial, and thence to 'real' use of LaTeX.
Tobias Oetiker's '(Not so) Short Introduction to LaTeX 2e', is regularly updated, as people suggest better ways of explaining things, etc. The introduction is available on CTAN, together with translations into a rather large set of languages.
Peter Flynn's “Beginner's LaTeX” (which started life as course material) is a pleasing read. A complete copy may be found on CTAN, but it may also be browsed over the web.
Harvey Greenberg's 'Simplified Introduction to LaTeX' was written for a lecture course, and is also available on CTAN (in PostScript only, unfortunately).
The fourth edition of George Grätzer's book “Math into LaTeX” contains a “short course” in LaTeX itself, and that course has been made publicly available on CTAN.
Philip Hirschhorn's “Getting up and running with AMSLaTeX” has a brief introduction to LaTeX itself, followed by a substantial introduction to the use of the AMS classes and the amsmath package and other things that are potentially of interest to those writing documents containing mathematics.
LaTeX, a Braindump (Internet Archive)
starts you from the ground up - giving a basic tutorial in the use
Linux to get you going (rather a large file…).
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.
D. R. Wilkins' 'Getting started with LaTeX' also looks good (it appears shorter - more of a primer - than some of the other offerings).
Nicola Talbot's LaTeX for complete novices does what it claims: the author teaches LaTeX at the University of East Anglia. The “Novices” tutorial is one of several introductory tutorials, which include exercises (with solutions). Other tutorials include those for writing theses/dissertations with LaTeX, and for using LaTeX in administrative work
Engelbert Buxbaum provides the 'slides' for his LaTeX course 'The LaTeX document preparation system'; this seems to be a departmental course at his university.
Mark van Dongen's 'LaTeX and friends' appeared as he was writing his book on the subject.
An interesting (and practical) tutorial about what not to do is l2tabu, or “A list of sins of LaTeX 2e 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). (in English, you may browse for sources and other language versions at convenient for you