It is possible to plug your laptop straight into your amp and mix using the dj software - either automix or using the onscreen crossfader. However automix generally sounds pretty bad, except for OTS and the onscreen crossfaders are awkward to use smoothly. It is easier to crossfade with a physical crossfader. There are a number of options with laptop djing involving combinations of controllers, soundcards and mixers, which make it tricky to get your head round at first.
It is possible to mix on a normal mixer, in which case you need (apart from the mixer itself) a multiple stereo channel soundcard such as the Gigaport or a 4.1 channel soundcard. You plug the soundcard into the laptop and then two leads out of the soundcard going to channel 1 and 2 on your mixer (or any two channels). This also means that you can cue one song whilst another is playing, like you would with cdjs.
Alternitavely you can use a usb controller to mix of which there are two types: those that contain a built in soundcard so that your sound comes out of the controller and into the amp/mixer, or those that don't contain a built in soundcard and so you will need a separate soundcard.
Bear in mind that even if you are happy doing the mixing on the software, you will need a mixer in order to plug in a microphone(s) and adjust levels and if you occasionly use a third source such as CD Player etc then a mixer is an absolute must. If you want to go the usb controller route, then you will most likely still need one, as very few controllers (save the Hercules) have them, for some reason, which I don't really understand.

I don't know what you use, as your backup plan, should your laptop fail, but if you use a couple of CD Players, Minidisc Players, Decks or even Ipods (dare I say it) for backup purposes, then should this become necessary, you would need a mixer anyway.