The first question I want to raise, is that of why. Why would you want to spend the money on a custom built bicycle, when the stores are now full of bikes that are getting nicer and more practical, and when there are vintage bicycles to be bought on the cheap? Here are the three main reasons I can think of:
1. The kind of bicycle you want is not available in stores.
This can mean many things, ranging from the basic form you want the bicycle to be, to its geometry, to more decorative issues.
For example: If you want a lugged steel touring bicycle, your choices for ready-made frames are limited to Rivendell and Velo Orange. If none of their models appeal to you, then going custom may be the only option. And although it may seem that vintage bicycles are available, it is actually quite difficult to find one with a comfortable touring geometry. Most bicycles from the 1970s- early 80s have fairly steep geometry and narrow tire clearance, do not do too well with a front load, and are more sporty than comfortable. Sure, you can set it as a goal to hunt around for a true vintage touring bike in your exact size - but not everyone is willing or able to dedicate the energy and time required for this. And if you are a woman looking for a true touring mixte, then it is more difficult still. Going custom allows you to specify exactly the kind of bicycle you want.
2. You are very tall, very short, or have unusual proportions.
Even if the type of bicycle you want is available retail, the sizes in which it comes may not accommodate your height or proportions. If you have long legs and a short torso, or the reverse, it can be difficult to find a bicycle that fits properly. And if you are very short, then adult bicycles might simply not exist in your size. A custom builder can build a frame in your exact size and tweak the bicycle's geometry to fit your specific anatomy. To a greater extent, this category also applies to people with special needs or handicaps - for whom bicycles with custom features or proportions could be designed.
3. You want a bespoke bicycle that is uniquely yours.
Maybe it is a special occasion in your life, or you are crazy about bicycles, or you are simply a person who likes every important item they own to be bespoke. Some people dream of that perfect wedding dress that is handmade by Polish lacemakers in a remote village, out of silk that comes fresh from the mulberry tree worm. Others never buy suits off the rack, but go to a tailor. Other still hire interior designers to create a personalised look for their home. Why not a bicycle then? If you find yourself obsessively doodling lugs shaped like butterflies and brake bridges carved with your initials, then for goodness sake - save up and get one built.
Finally, if you are wavering between that mass-produced bicycle that is not quite what you wanted, and a custom bicycle that is perfect but costs $X00 more, consider the differences in value and longevity, and in the subjective pleasure you will be deriving. Consider also that in buying a custom frame you will be supporting a local economy and an independent artisan, rather than funneling money to an anonymous manufacturing corporation. Whether these factors justify the extra cost is entirely up to you - but certainly something to consider.