I've used cardboard boxes as checked luggage several times, including to transport desktop computers twice.
Most likely the airline will make you sign a waiver that you accept all responsibility for any damage, but otherwise you'll have no issues as long as it's within the allowed weight/size guidelines (which if it's just a computer, it will be).
I didn't bother with any extra padding/etc, on the basis that the original foam in the box fitted the computer perfectly. I did make a point to wrap the computer completely in plastic (eg, the plastic bags that they normally come in, or something similar) and then seal the bag with tape in an effort to make it somewhat waterproof - obviously not enough that it's going to handle getting dunked in water, but enough that it'll survive getting rained on whilst they are loading/unloading the plane.
Fragile stickers certainly wont hurt - I actually use "fragile" tape that you can get from Office Depot or similar and just run it around the box a few times.
If possible, try and pick flights that are on a wide-body aircraft (747, A340, etc) as cargo on those is generally treated a little better than on narrow-body aircraft where it's manually loaded into the hold, rather than being loaded in crates.
And just remember that at the destination airport you'll probably need to go to the "oversized" baggage area to collect it rather than getting it on the normal luggage belt.
Update: I once again traveled with a checked-in box from the USA to Australia just before Christmas. On this occasion the box was opened by the TSA for a security check - however I'm happy to say that they did an excellent job of opening and re-sealing the box. Other than the note they put in the box and the fragile tape obviously being cut there was no other indication that it had been opened. Everything was still packed exactly as I had left it, and they had sealed the box just as well as I had.