Hi,
I'm looking for an amplifier for my PC.

I'm thinking about buying a couple of "cheap" but good speakers from Hi-Fi Klubben (http://www.hifiklubben.com/DK/Produkter/Hoejttaler/Kompakthoejttaler/ARGON_6110S_hoejttaler_Ahorn.htm)

For that I need an amplifier, but is there one that is cheap, small and can drive these speakers?

Well, I would look on eBay for used amps. Something from Harman Kardon, Pioneer etc...you name it. Buy an old amp which used to be medium to high-end for around 100$ and you should be fine.

With speakers that small about 30 watts should suffice (even with larger speakers 30 watts is often more than enough...).

If you really want something new you may take a look at the Pionner A-109 or the Yamaha AX-396/396 you should get both for < 150$.

Hi, thanks a lot for the reply, but isn't there a more elegant solution? Like, something smaller in terms of XxYxZ measurements.

How about this by Sonic Impact.

http://www.si5.com/products.php?pID=4038

Well it's hard to buy a "real" hifi amp with smaller measurements, as there is a standard form factor for these devices. You could try to get an amp from a compact (micro) hifi system such as the Yamaha Pianocraft etc, these will be smaller but are normally not sold stand alone (as far as i know) but with speakers/tuner/cd-player so your only option is to look for used components on eBay or sth.

If you look at the datasheet for this cards chip you will find it will only deliver 10 watts or power at reasonably distortion leves. If this is enough, fine, but remember that you need 10 times the power for twice the loudness. As his speakers have an efficency of 85db you can reach a loudness of 88db in 1 meter distance.
Now if you ask how loud this is - workers have to wear hearing protection if the are exposed to sounds > 85db (at least here in germany), so it is fairly loud, but wouldn't try to make a party with this setup.

Now that you mention Sonic Impact, they have another nice amplifier the T-Amp. It had several rave reviews (6moons Audio, TNT Audio) and alot of people are customizing their amps with DIY cases. Sonic Impact did a new version of it with integrated power supply and a nice looking case, tough I find the price tag a bit high for this version.
But again, this amp will also only deliver about 10 watts of clean power. With high efficeny speakers this is sure enough to shake the walls, but with these small speakers I don't know.

Considering the low price of both the card linked by NappyHead and the T-Amp you could of course just try it out and see if it works for you.

Other than this, there's a nice DIY scene around the Gainclone, you can buy kits and design the enclosure any way you want (here's a nice one), but I wouldn't consider this a project for beginners. Maybe you could buy an already finished amp on eBay (I found one) or ask in DIY forums such as http://www.diyaudio.com.
http://www.audiosector.com/ is also selling finished amps but I think they cost more than you are willing to pay.

It's really hard finding something with small measurements which is still high quality stuff. I had the same problem finding an amp for my girlfriend and ended up buying an Akai Amp from the 70s, after some restauration work it still plays like new .