This may be a little too much hands on for many people who would prefer to simply buy their AR15. However, for those of you who are even the least bit mechanically inclined and have the time to spend building an AR15, I highly recommend it.
I like to say that if you can change your own oil in your car, you can build (or assemble) an AR-15.
Simply put, the best reason to build your own AR15 is so that it can meet your exact specifications and so that you can customize it and make it your own. I like that it gives me the ability to know and understand the design and function of the AR15 rifle. This gives me a better idea on how to diagnose potential problems and fix them.
It also gives me the ability to hand inspect every part in the weapon to determine quality (to some degree). I can swap out and upgrade parts as well as refinish them in order to improve quality of the part and the weapon as a whole.
It’s also nice to be able to make changes down the road when I decide that I want a different upper style, barrel profile/length, etc…
There are various degrees of AR15 building. Anywhere from buying two separate halves (a complete upper and a complete lower) and mating them together (the easiest way to “build”) to finishing out an 80% stripped lower and turning down a barrel on a lathe (something that takes a lot more time, tools, and savvy).

A complete AR15 carbine lower receiver.
I read an article not too long ago about the downsides of what some people refer to as “frankenrifles”, home built, or even kit AR15’s. It went on to mention that these rifles were not reliable and should not be trusted for personal defense.
While I agree that many of the cheaper “kit rifles” may be lacking the quality, a home build very well can give a savvy AR15 builder a better rifle than can be purchased off the shelf. However, this starts with using quality components from reputable companies, especially where it matters most.

A custom built 14.5″ AR15 carbine (with a permanently attached 1.5″ Phantom Flash Hider), Hogue grip, CTR stock, LaRue rail, and ACOG (light sabre not included)
Many people often think that you can save money on AR15’s by building them, this can be true but it tends to be most true when you desire to build the best possible rifle for the money. This is because you can buy many parts such as a forged anodized lower receiver from many reputable companies for much cheaper than if you went straight to LMT or Noveske. Most AR15 lower receivers are going to be the same in quality, regardless of manufacturer. The same is true with many other parts.

AR15 Carbines refinished with Duracoat in camo pattern.
Compatibility between various brands usually is a non-issue. Once in a while, you will get an upper from brand “X” and a lower from brand “Y” that will have a tighter and looser fit.
A tight fit is usually cured by usage of the AR15, shooting, assembling and disassembling. A loose fit can be cured with an Accu-Wedge. Sometimes the finishes will not match perfectly (this is merely cosmetic and will not affect the function at all). Receivers can have anywhere from a black, gray, or even purplish coloring depending on the manufacturer and the particular “batch”.
Refinishing is an option if this bothers you that much. Of course, there is also the option of swapping out the receivers. Fit and finish is nice, but it doesn’t translate to anything where the rubber meets the road.
Having built several AR-15’s, I can say that there is very little problem using parts from different manufacturers to construct an AR-15. I have rarely assembled an AR-15 with all the parts being from one particular manufacturer. Most of my personal AR-15’s are mutts.
A few things you should know about building an AR15 Federal law Prohibits you from building a rifle with a total barrel length of less than 16″ unless you apply for and are granted the $200 tax stamp for an SBR (short barreled rifle). If you do not have the tax stamp and intend to put the upper on a rifle lower that is not registered with the ATF, you must be sure that your barrel is the minimum required length. In order to achieve this minimum length on a shorter barrel (than 16″) such as a 14.5″ barrel, you need to permanently attach a muzzle device that will bring the overall barrel length to 16″ or greater.
A pistol AR15 CANNOT have a buttstock or a vertical foregrip. A registered SBR can have a buttstock and a barrel of any length.
Although I oppose many of the laws regarding restriction on barrel lengths, select fire capabilities, etc. I do NOT recommend or condone ANY illegal modification to your AR15. It is simply not worth it.
Disclaimer: Some states, cities, and counties make it illegal to own certain configurations including but not limited to SBR’s and NFA. Check your local laws to be sure that you are in compliance. I am not a lawyer, nor should I be considered an official source on laws in regards to AR15’s. I do not accept responsibility for any illegal actions taken by the reader through misunderstanding of my writings, the readers lack of research, or otherwise.