Forgive me for this, but this is an element I'm pulling from various other games. Moving elements of the HUD individually, while a programming nightmare, would be a major benefit to players I believe.
The element in particular that inspired this is the "raid bar" on the left of the screen. In past games, I would often place this centrally on "support" characters for ease of use in buffs and healing (typically with semi-transparency). SO much more reliable than attempting to click on characters. How often has someone missed a heal because their carry juked it by accident?
This should not only include moving elements, but adding and removing them as well. If I'm playing an AP mid, I don't care what my AD is. I would rather have something like CDR or Spell Vamp on my stat bar. Some champs, I would gladly remove this bar entirely for more screen real-estate.
Since certain configurations would not help some champions/roles and even harm others, I believe saved configurations should be added as well.
This is not a stab at the current UI to say it's bad in any way; only that a single UI configuration cannot support the needs of all players.
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EDIT: A few moments after posting this, I ran across something called the ACE client that seems to do this and more. How reliable, stable, updated, and more importantly "legal" is this?