Here they are for building your own PC.
Pros:
You can fully customize what you want in the system from the case color to the cpu.
Its more fun to build if you know what you are doing.
In most cases its cheaper to diy rather than buy a Dell or something.
If you are into gaming, its definitely cheaper.
You can install what you want on the system, and not have something preinstalled that you don't want *cough*Vista*cough*.
You can also overclock your system without any restrictions..not something I do usually but it works if you have the right cooling equipment.
You know whats going into the system for components.
Everything is upgradable if you get the right motherboard and parts.
Cons:
Can be problematic if a random part fails or is defective. Same goes if you're a beginner, in other words if you aren't experienced.
More of a hassle if you don't like to shop online.
Not much of a warranty, just warranties for parts.
Can be more expensive if you can't buy online.
You also have to buy or get all your own software and os.
Incompadibility issues with hardware and software.
I haven't really bought a premade computer in a long time except for a refurbished gateway laptop last month, but here are the pros and cons on buying a system from my perspective.
Pros
Bascially everything is built and made for you to work out of the box.
Can be cheap if you aren't looking for a powerhouse.
The warranties can really help if something fails.
Comes with its own software and OS.
Usually all the accessories you need is included like keyboard, mouse, etc.
There's usually customer service to help with certain things.
Cons
More expensive in most cases.
Depending on the brand, the customer service can be shady.
Vista is installed on pretty much all new PC's without having a choice. There are only a few brands left that let you use XP for an OS.
Some of the software preinstalled can be useless.
Can be lacking in overall power and ram.
Upgradablilty is usually limited.
More restrictions on the bios.
Quality control can also be shady.
Extended warranties can be expensive and useless in the long run.