Welcome to Tom's Hardware,
You can easily build a better computer for less than an Alienware but you won't get the support Dell provides.
I threw together a more powerful build for about $50 less at PCPartPicker here - it is overkill for a gaming rig - http://pcpartpicker.com/ca/p/vp0W in about 15 minutes although there are differences which rarely might be better on the Dell. The Dell uses a Socket 2011 motherboard which does allow for 4 channel memory, the Socket 1155 (I chose) only has 2 channel memory. If considering adding additional video cards in the future, the 2011 board allows for full bandwidth through all PCIe slots, the 1155 board is limited to half speed on the second slot. (which covers all the differences). Now I'm going to show you a Monster gaming rig (also on PCPartPickers) for about the same as the alienware, nope still short http://pcpartpicker.com/ca/p/vpib or even this (better) http://pcpartpicker.com/ca/p/vpoK for $55 more than the Dell
For boutique builders there is CyberPowerPC http://www.cyberpowerpc.com/category/intel_pc/ note that the X79 builds (socket 2011) start at a lower price point than Alienware but the price does not include the operating system installed so figure another $100 for that
If you would like, I will explain my choices but I think that should be enough to absorb for now
I have some time so I thought I'd share my thoughts on why the choices of my builds
First thing to note is they include a small SSD for OS/boot drive
Second, they both have better graphics cards
Third they both have better quality PSU's
Both have all-in-one liquid cooling for better overclocking
The biggest difference is in the CPU with the Alienware sporting the Socket 2011 i7-3820 while my builds use the i5 3570k. Here's why, gaming currently does not take advantage of the technology the i7 has over the i5 which is hyperthreading (the ability in essense of creating virtual CPU cores). You would be paying for something you don't need. Also my builds have the ability to overclock, not that you have to do that but it comes in handy on many games. It's good to have the option later... I can't count the threads I've read where people were disappointed to find out the system they had purchased was 'locked' and unable to be overclocked.
Again, My $0.02