Reitterating what Suo said in my own words and opinions;
1. GPU is the most important. Mid tier cards are best performance/cost, and can do everything required of them now.
2. Ram is pretty important - to a point. 2-4gb is recommended, after that it's more or less just for fun.
3. CPU is WAY overrated, most games can ONLY use 2 cores, so quad core is wasted. Most games will happily use 2.0ghz or less, so anything above a dual core 2.0ghz is wasted (2x2.0ghz is considered very low, so its not like this is a big ask. Most gamers will pick a quad core 3.0ghz i7 when it is really 10x more than they will use)
4. Harddrive - to an extent. Harddrive speeds are like paying your bills, its not a big deal so long as it all happens in a timely fashion. If your harddrive is too slow then your whole computer will suffer. Of course, a 64gb SSD (which is plenty for what most users would need) will set you back just under $100 (@Suo: I recently bought a 64GB Crucial RealSSD C300 Solid State Drive (265MB/s, TRIM) for $80. Decent, no?). If you have plenty of RAM then you can map it as a harddrive and mirror things in to the RAM disk for great speeds, but a bit of hassle. This won't be too helpful for most people, but it is useful once you hit the 'soft upper limit of upgrades' for CPU, GPU and RAM.
5. Network speeds are very important, make sure your network card is up to scratch (it shouldn't be too hard, with network cards being easily in the range of 50-100MB/s whilst internet speeds being in the range 5-10Mb/s), and you get a good internet provider.
6. Keep your computer clean - just because you have all the latest hardware doesn't mean squat if your harddrive is 90% fragmented and 90% full, and you run 120 programs on startup which sit on your CPU burning 1-0.5% each, and you fail to optimize your performance and keep your drivers updated, and your computer disinfected of viruses. Just remember to do a de-fragmentation once a month (a week is better, but whatever), and a full system virus scan (once a week is better too), and keep your drivers up to date, and kill any programs that autorun that you do not use.