Is Budget Cycling Apparel And Equipment A False Economy?

As road cycling is a very tech-based sport with countless companies all trying to deliver the most amount of value, it's unsurprising that the race to the bottom can result in substandard products.
So what products should you be avoiding when out looking for a bargain? When is it best to spend a bit more to ensure that you aren't left with something that will cause more pain than happiness?
Sam Gupta lists what he thinks are some of the biggest false economies in road cycling and the cycling products which you should avoid.