I can contribute describing the differences between Keynote, Impress and LaTeX Beamer. Previous answers only seem to have second hand knowledge of what Keynote can. What makes Apple Keynote "so cool" are the smart guides which let you align stuff with great efficiency and speed. It also handles all kind of media files and is still extremely fast at it.
What's key for a presentation software is to have very little lag when presenting slides. If the user presses "next slide", but the software is struggling to render the frame prompting the user to question if the "next slide" command was registered, maybe triggering it again, which then makes the software skip two slides ahead... these kind of situations can confuse and frustrate a presenter enormously and Apple Keynote has covered this element in perfection. No matter how large the graphics or media is, the next slide will always load instantaneous.
In OpenOffice/LibreOffice you need much more clicks and sub-menus to align graphics or text. Once you have added images which have a slightly higher resolution it becomes unusable and slow to the point that you just hate to work with it because you are spending time on waiting for it to save the document. Trying to embed video files is even worse. A document with > 10 high-res images in it will be so slow that you can't do a presentation with it.
The LaTeX Beamer class templates look terribly scientific and are not usable for presentations outside academia and research just because of their graphic design (some notable exceptions exist, for instance hsrmbeamertheme has a refreshing look). Sure you could make your own styles, but typically presentations are done with very little time, and you just want to throw some things in, not modify styles just to see how it looks when you have three pictures on one slide instead of one. This is where Keynote shines. Efficiency, ease of use and speed.
You can use the Free software Scribus to create your presentations as PDF documents (Scribus now even has smart guides). For the presentation itself I employ the pdf-presenter-console package (unmaintained, but in the repositories, updated version: pdfpc, for a nice feature set but sadly abandoned check open-pdf-presenter). You might also want to look at Impressive for on the fly highlighting and transition effects (but no presenter screen support). PDF presentations generally don't allow videos though, which can be a huge drawback compared to Keynote.
If you are working with video or audio files, be prepared that you will have to jump through a few hoops on Linux. No program will allow you to set in- and outpoint, set autoplay on or off and adjust the volume level for each media item. Open/LibreOffice will just choke and become entirely unusable. Inkscape never the less can be one way to make a multimedia presentation. You can use it to create presentations either with the JessyInk extension (which comes pre-installed with Inkscape), or with Sozi, a program that lets you create Prezi-style presentations (zooming and panning on one big canvas) from a SVG document. Both are solid, you can embed media (audio, video, links) as well as mouse roll-overs and so forth. Presentations happen in a browser (full screen mode, no presenter screen). The types of media files and codecs you can play back depend on the browser you use.
Another option is to use browser based presentation frameworks like reveal.js. It handles media and even offers a presenter screen.
If you don't mind a proprietary solution you can use WPS Office (previously known as Kingsoft Office). Here you can put videos on the slides and it shows a controller for the media on rollover. You can also trim media files, but not set a custom audio gain per media file like in Keynote.
OpenOffice
LaTeX Beamer
Scribus
Inkscape
reveal.js
PresenterScr.
Yes
depends*
depends*
No
Yes
Audio/video
Yes
depends*
No
Yes
Yes
Animations
Yes
depends/some*
dpns/sm*
Yes
Yes
Subjective qualities:
Ease of use
Okay
inflexible
Good
Good
Okay
Performance
Unusable
Good
Good
Okay
Good
*
Depends on capabilities of PDF viewing/presenting application and is platform specific.
Update 2019: OpenOffice and now LibreOffice have become much better and performant even with large media since 2013. However embedding Video is still not en par with Keynote.
Update 2021: Sadly still no real contender to Keynote for Linux users.
Update 2023: LibreOffice has become much better, and I've used WPS-Office Presentation on Linux and this is actually usable.