Battle Athletes.  The character designs are very 
different from the OAV to the game to the TV 
series; I know I'm not alone in collecting only 
the TV series because that has the best designs.  
(And, well, the TV series was way better than the 
OAV anyway). El Hazard's designs also change from 
the OAV to the TV show; that actually seems to be 
standard procedure for the AIC/TV Tokyo stuff (BA, 
El Hazard, Tenchi).  Utena was also completely 
redone for the movie (which again is very 
different from the manga design).  Then there's 
the wide range of stuff where the manga looks 
totally different from the animated work (Sailor 
Moon's a big one).

Why change chara design?  In the case of 
manga/animation, it's probably because the manga 
designs are often more elaborate (and 
therefore harder to translate to repeated 
action drawings) than the animated forms.  I can't 
imagine seeing the weird swirliness and sparkly 
quality of the SM manga actually animated exactly 
as it looks on paper.  

In the case of switching design from TV to movie 
to OAV, I'm guessing they do that to diferrentiate 
the forms--note that in every example given of a 
style change, the newer product is either a 
retelling or alternate version of the existing 
timeline, not a direct sequel/prequel.  Having a 
new character design says "this is a different 
story from the one you've seen before."  (As a 
side bonus, it makes it easier for those of us who 
want cels from one form of the anime but not 
another to pick out which cels we'd like to buy 
and which to pass over).