I just bought a frame and built it up (my 3rd or 4th frame I've done now). The positives: you'll have loads of fun, and possibly get the components you'd really want; the negatives: it usually is as costly or more costly than buying that bike with the specs you wanted in the first place.
Obviously much depends on how you want to spec it (e.g. Tiagra or Dura-Ace? Deore or XTR?) or which components you have already. Cost is so variable (e.g. I've seen flat bar mtb Deore shifters for 9-speed on craigslist for $20, cheapest STI 9-speed I've seen? $70. We're talking over 300% cost difference here, so I think you can see it's difficult!). Ebay and Craigslist could be your best friends here. Assuming you have absolutely no components, I'm guessing you'll have to spend at least $500 to get reasonable (very subjective here too) components, and that's if you are incredibly lucky and buy many things used. Some people may think that figure is overblown, some will think I'm being way too optimistic.
I've outlined a list of tools below -it should include everything you'd need (I'm sure I've forgotten something though). A word of warning: you can seriously damage you bike (e.g. cross thread the bb) so if you're not mechanically inclined, I don't recommend you do it. Additionally, as you read the not insubstantial tool list below, you might guess some of the tools are not going to be cheap, and it could be better to just pay your LBS to do the work -particularly if you're never going to be building a bike again or anticipate doing one every 20 years or so (that's not me, by the way, which explains why I've invested in so many tools). On the positive side, mechanical aptitude will get you a long, long way, as well as a good dollop of care, common sense and caution. And of course, there's nothing like the satisfaction you get when you ride that bike you built yourself, let alone knowing 100% how you did the job rather than some of the bike "mechanics" in some of the stores. It's also good to know that if you need some work done on your bike, so long as you have the time, you can do it immediately rather than being dependent on someone elses schedule. Obviously, a compromise could be to buy a limited number of tools, do some work yourself and then get your LBS to do the rest.
Tools (assuming you do *everything* yourself):
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Headset press (you can use a hammer and a block of wood, or make your own with a large bolt and many different kinds of washers, which is what I've done, and had perfect results everytime).
Headset remover (you can use a plastic pipe and a nut and bolt for this -plus you only really need this when you have to remove a headset).
Race setter (if you have a Orbit headset, they have races you can put on effortlessly, otherwise a sub would be a pipe of the correct diameter with protecting washers and judicious use of a hammer).
Starnut setter (assuming threadless headset -but you can use a hammer and screwdriver -for ease of use, I use a starnut setter).
Steerer tube cutter (you can buy an expensive "bicycle specific" saw guide, or alternatively use a pipe cutter)
Crankarm remover (can't think of a substitute here, you just need one -at least to get pedals off, so maybe strictly you don't need one to build a bike!)
BB installer/remover tool -(again, don't think there are any subs on this one)
Cassette whip tool (can use an old chain for this, judiciously wrapped with cloth to save your hands -for the expense and to save my hands, I have a whip tool).
Cassette remover/installer tool (no subs!)
Generic stuff:
good quality torque wrench (now you don't want to strip the threads in your bb, do ya?)
good quality grease/lubes
degreaser/mineral spirits
anti-seize or similar for steel to alu interfaces
chain splitter (if your chain is not SRAM or similar with the removable link)
cable cutters (can be bought from a hardware store)
Allen keys
wrench (for bb and cassette tools)
screwdriver (for adjusting gears)
pliers (sometimes handy for pulling cable)
hammer/rubber mallet
Really nice to have:
Bike stand
Misc.
Cable ends/cable donuts/cable nipples
Bike repair book (though you can get info online including torque settings)