I know that PCI express x 16 is ideal for top notch video cards, but what is PCI Express x 1 used for?

There are various uses for the slot, including: usb add in cards, firewire add in cards, sata add in cards, networking(ethernet) cards, and even a graphics card for x1 slots.

http://www.newegg.com/Product/Product.asp?Item=N82E16815124032
http://www.newegg.com/Product/Product.asp?Item=N82E16815158036
http://www.newegg.com/Product/Product.asp?Item=N82E16815104264
http://www.matrox.com/mga/media_center/press_rel/2005/millennium_g550_pcie.cfm

And if your next question is "why not use PCI-E 16x", then the reason is pretty plain: it's cheaper. 1x requires 16 times less circuitry saving a lot of PCB and silicon real estate.

Is PCIe x1 really faster then normal PCI 2.1?
I mean would networking card or video for PCIe work better then the same card for PCI?

A single PCI-E lane is about 2x faster than PCI. PCI-E is also full duplex, meaning that if you send and receive at the same time, a 1x link can be up to 4 times as fast as plain PCI.

Another question

So, besides graphics card, what other card would really benefit from the faster architecture? TV tuners and Firewire?

Anything can benefit from PCI-E.. Since PCI-E is not a bus, every device on it has a full-duplex dedicated link - no more waiting behind each other to transfer data.

Are you talking about that small 2 CM PCI port? If so, then I ask the same question.