Basically, it seems like there are a lot of underused champions and worthless skills out there that could be tweaked slightly to make them "better". There's a rough consensus on which champs are not used in high level play, and a general understanding that buffing them in the wrong area could make things un-fun for your average Joe.
So this thread is my own personal brainfart on minor changes to champions that would hopefully even the playing field.
Issue the First- Teemo
In low and even mid level play, Teemo can take the role of a decent-ish carry. But as you get matched with better players, he starts to pale in comparison to Tristana and Twitch because of his lack of strength or utility in team fights. He also has one Pink Elephant of a skill in Move Quick, which is generally not useful beyond the first level and annoying to keep re-activating.
To give him slightly better utility, change Move Quick as follows.
The current Move Quick ability would be re-jigged into a passive along the lines of Boots of Mobility. No mana cost to reactivate, instead it does so automatically after 5 or 6 seconds out of combat. The active version of the skill would have a decent sized cooldown (20-30 seconds) and boost the move speed of all champions within a small radius (think Alistar's Roar) for a brief amount of time (nowhere near as long as Sivir's ult.)
Now instead of being an inferior alternative to Tristana or Twitch, he has a second useful ability in teamfights by providing a quick sprint to a couple other teammates.
Issue the Second- Veigar
Veigar has the potential to be truly monstrous, but his high mana costs and awkwardness of landing Dark Matter make him pretty bad in the early game- nowhere near the level of Annie, Ryze or even Kassadin (since Kassadin's main damaging spells carry nasty side-effects.) Aside from his pentagonal stun cage no I can't remember the name of it he has nothing to give in a team fight once his ult is burnt- and with Flash potentially nullifying it, he's the red-headed stepchild of casters.
Buffing him is not an easy thing to do without making him a hard counter to casters. Hard counters are bad.
To make him more viable early game, the obvious thing to do is lower the mana cost on Baleful Strike. It's ridiculous how easy it is to empty your mana pool just trying to do the one thing the modus operandi of the character encourages.
To make him more viable in team fights... well, this is harder. But Dark Matter is the key here- while Ryze can throw out an insane ult'd Spell Flux, and Kassadin can spam Force Pulse, and Annie can AoE stun... Veigar has one spell that's going to hit, one spell that's up every 2 minutes or so, and one spell that you'd be lucky to peg anyone half-decent with barring stun spam. The delay between casting and it landing is far too long- lower it!
-More to come-