Related question: Can I do this for a laptop?
No, don't even try. Gaming laptops are terrible, and custom-making one would be more money than it's worth.
They usually all have the same problems. They overheat hot enough to the point you can cook eggs on it in a short time, the battery life is ridiculously low, and you're essentially paying a lot of money for a mediocre system when you could of used that money to get a top-end system.
While this IS true, if Chairman's situation is anything like mine where I need to have a portable computer, like to play games, and don't have enough money for a desktop and a laptop, you *can* find a good gaming laptop out there, it isn't impossible (but seriously, don't even try to custom build). You are going to end up spending a whole lot more time finding a decent gaming laptop than you will spend building a decent gaming desktop. A must have for any gaming laptop is something like Nvidia's Optimus, which turns off the GPU when you don't need it so your laptop lasts longer than an hour, and numerous hours of reviews between 2 or 3 laptops that are all virtually the same, except you find out that 1 or 2 or all of them have overheating issues. My current laptop afaik is a pretty good one considering I spent $700 and bought it in store when the model had just came out, and it never overheats (I sometimes play games with it sitting on my lap while I am laying in bed with the covers propped up around me, and it never goes over 80c). Stock battery life was shitty, 2 1/2 hours (and the battery was at 75% capacity when I bought the laptop due to improper storage -.-), but I bought a 9000 mah battery for it and it now lasts about 6 hours as long as I'm not gaming (and I'm not needing to game when I am using it in class), so plan on buying a new battery that has a higher capacity and storing your old one for emergencies (stick it as close to 0c as possible at 40% level and take it out once a month to make sure it stays at 40%). It isn't the most powerful gaming laptop by any means, but it runs everything at playable frames even if it looks a bit shitty. Overall I probably spent $860 on it after upgrading the ram and the battery. I couldn't spend $860 to get a portable machine and a gaming desktop that would work better than what I have.
More on topicish, pretty much everything in a desktop is important, right down to what compound you use for your heatsink. Without nitpicking, for gaming you probably want (assuming you are using 64bit) 8gb of *good* ram, because 8gb of good ram will go a long way versus 12 or 16 of crappy stuff (good meaning good clock speed and latency). GPU wise, consider possibly doing SLi or Crossfire (though I have heard crossfire causes stuttering like a madman), because you can spend the same amount as a great GPU and get more performance (though it will heat up more, and you will need a better PSU). Some games don't support SLi or Crossfire, or either though, so it might also be better to just have one great GPU. For CPU, I really can't add much because I am an Intel fanboy and everyone here seems AMD (personally I like AMD better, but I've been using laptops for a while and I can't find a good laptop that uses an AMD cpu), but for gaming, the latest i5 or AMD equivalent would probably be fine (either the one that has hd 4000 or hd4600 (even though you should never be using the integrated craphics). An i7 might seem like it will get you a whole lot more performance, but unless you commonly play games that use your CPU a lot, it won't really net you much visibly. PSU you want anywhere between 120% to 150% of what you think you are going to use, depending on if you are going to OC or not. If you plan on overclocking, make sure your case has plenty of cooling support, and buy better heatsinks than stock. There's more but I gotta go so I'll just leave this here.
edit:
I wasn't particularily thinking on a "pure" gaming laptop (albeit what I have in mind is buying one that can run some decent games at a good pace -eg: DF, C:DDA, Torchlight 2, Warband-). And I was wondering whether custom-buying it via PCBOX or simmilar services would be better (eg: cheaper) than getting a factory one. My idea was to spend about 600-700€.
Are you looking to play those at high graphic levels and good FPS, or slightly shitty graphics and good FPS?