None of the answers posted here really solves this common problem, which apparently is difficult even to explain, due to too many irrelevant details, and sometimes unreasonable requests or explanations, often posted along with it, which make it frustrating even just reading this and other forums looking for a solution.
I'll try to explain the issue I'm having, which I'm sure is the same as almost everybody else, in clear terms, in 3 lines:
Long ago I've bought several, relatively expensive, apps with an old Apple ID.
I then created another Apple ID, and bought (many) more paid-for apps under it.
Now I want all my purchased apps under my new Apple ID, because I'm absolutely SICK of having to switch IDs all the time to check and get updates, and of course I don't want to pay for them again, as this would be unfair.
The problem IS NOT the free apps: I can just download them again under any ID, at any time.
The problem IS NOT having the same (paid-for) apps under more than ONE Apple ID: that'd be just confusing, and still that's what some seem to be asking.
The problem IS NOT having the same (paid-for) apps available to more than ONE USER (as in "person", ie. authorised PC) while only paying once: that'd be unreasonable, and yet it's what some seem to be asking.
The problem IS NOT switching IDs in iTunes or the iPhone, which seems so difficult for many: just sign out from an ID and back in with another, if you like complicating your life as I'm FORCED to do by the Apple store's silly ID policy.
The problem IS: moving (merging) all my purchased apps between two Apple ID that demonstrably belong to me, in order to have all my apps under one Apple ID only. This ought to be possible. Apple gurus: HOW TO DO THIS, PLEASE?
Of course when I created a new account I was blissfully unaware that the Apple store links the apps to the Apple ID with which a user happens to be logged in at the time of the purchase/download, rather than to the USER, via the authorised PC: otherwise what's exactly the purpose of authorising a PC? This critical information is nowhere to be found, until you infer it when you stumble in this problem, of the course.
The fact that the Apple ID is an email address, which seems disposable by its very nature, leads many people (like me) create and use more than one without knowing what they're in for: I actually thought it was only for receiving emails from the Apple Store, NOT for authorising (ie. locking) my purchases: this isn't explained anywhere.
If Apple doesn't let me manage MY OWN legitimate purchases in such a trivial way as allowing me to have them all under ONE account, to be able to update them all easily, without effectively being FORCED to constantly switch IDs just to check (!) for updates to them, then their system is very poor and an incentive to use something else, and better.
The option that is sometimes suggested by Apple staff, to download them under the new ID and PAY AGAIN for them, is just an insult.
(a frustrated user)