I went through and checked, and the following REALLY need new icons. Many haven't been altered since Beta.
I know Anivia and Janna got new ones but they never got implemented for some reason.
On an unrelated note, splash art wise, the following could do with an update as well...
And I know Irelia/Warwick/Swain have or had one in the works
I didn't put Taric on here cause his Soon(tm) rework
akalis and ezreals is fairly new compared to the rest atleast
Can't improve on perfection. Many of these icons are great looking as is.
and already have new ability icons but those have not been implemented yet
has new ability icons currently in the works, no ETA for them tho http://boards.na.leagueoflegends.com/en/c/story-art/h51wa3LI-riot-champions-with-outdated-ability-icons?comment=000000010000
some ability icons will get updated for the "mid-year" mage update, these icons could be for 
, , 
and 
