They say Inkscape is an SVG editor. I don't really know what SVG is. I need something like Adobe Illustrator, Corel DRAW or Xara Xtreme. Is Inkscape good for me?
Yes, officially Inkscape uses SVG as its internal file format, and SVG is a vector graphics file format designed by Web Consortium (W3C). This is easier to stick to a standardized file format than to reinvent the whole thing. SVG is XML based and thus is basically a text file, so you don't have to deal with a problem of corrupt files the way people deal with e.g. CDR.

However what Inkscape developers really do is a feature rich illustration tool that is fun to use.

It's quite possible that you will never look inside an SVG document. Or maybe (if you are web developer) you will do it all the time. This is entirely up to you.

What's unique in Inkscape? Did it really make sense creating yet another vector graphics tool?
There are not so many vector graphics editors, and most serious tools are part of the market for 10 to 20+ years. But this means that their developers are doomed to keep layers of legacy solutions and build new functionality on top of them. If you have a look at e.g. ACD Canvas which has duplicated tools, 3 tiers of toolbox, or at Adobe Illustrator, where e.g. editing, adding and removing nodes are three different tools. you'll see what we mean.

Inkscape as a project was started in 2003, so developers had a great chance to keep in mind disadvantages of other tools and avoid the. Which they did. That's about usability.

As for functionality, Inkscape has a pretty interesting set of features, some of them unmatched in other software. For example, pattern of clones: clones of an original object are laid out using any of 17 symmetry groups with optional offset, scaling, rotating, color and stroke changes. Or Callygraphic pen which can be used to imitate engraving.

Or the bucket fill tool that creates vector objects matching closed shapes of both vector and bitmap graphics.

All right then. What file formats are supported?
Inkscape imports AI (v9+), PDF and EPS (Linux and Mac OS X only) fairly well. Besides, with UniConvertor installed you can open various Corel DRAW files (paths, flat fill and stroke supported right now) and WMF. The upcoming v0.47 also features a rather improved DXF import filter.

Documents can be exported to PNG, PS, EPS and PDF. Web developers might be interested in Microsoft XAML and JavaFX (v0.47) exporting too.

Wait, so I can't save to CDR?
This is a question to UniConvertor developers :-) As soon as they have this feature, Inkscape developers add this feature too. But since Corel DRAW actually opens SVG files, you can simply save to Plain SVG and pass it on. Plain SVG is the very same document, just without extra features that are not supported by Corel. The document will still be rendered correctly.

What about Pantone? CMYK?
Pantone will not allow redistribution of its palettes. However most recent development version of Scribus can use Pantone's official EPS palettes, so it is recommended to use Scribus to do color separated exporting to PDF using spot colors (read on).

I do icons and other display graphics. Is Inkscape the right tool for that?
We recommend investigating Jimmac's one-canvas-workflow.

I've used Inkscape a little and I just can't get used to its shortcuts. How can I use shortcuts from e.g. Illustrator?
Yes, and not only Illustrator. You can use shortcuts from Corel DRAW X4, Xara Xtreme, ACD Canvas 11, Zoner Draw 5 and Macromedia Freehand MX, but only where they match Inkscape's funtionality. You need to copy the correspondent file from /usr/share/inkscape/keys/ to local directory ~/.inkscape/keys/ (~/.config/inkscape/keys) and name it default.xml. However keep in mind that using Inkscape's native shortcuts is still better in the long run. So why not take a time to learn them?

I went through tutorials available from Help menu. Are there some cool 3rd part tutorials? A full user manual? Any books in sale?
We have several cool Inkscape tutorials for you. The ultimate blog listing tutorials is here.

There are books in English, French and German (check Amazon), and there is a project to create official user manual in multiple languages. The first revision is available already. Please read Documentation page at inkscape.org for details.

Where do I download Inkscape
The best place would be Download page at inkscape.org.