I think a Grass/Dragon type would be quite interesting (and it would still be 4x weak to Ice).
Grass/Ghost would also be an interesting addition (a withered/wilted plant, perhaps?)
Someone earlier mentioned a Grass/Fire Pokemon (heh heh, Burning Bush? Brush Fire?), and I think that'd be amazing, as it would remove Grass' weakness to Fire, Ice, and Bug and Fire's weakness to Water and Ground. Give it good stats and you'd have a very competitive Pokemon.
Psychic/Ghost and/or Psychic/Dark would also be another amazing type combination.
I think that a Ground/Fighting type would be nice to have competitively as well, hitting with STAB Earthquake and Close Combat (if given those moves).
Steel/Ghost would make for a very impressive tank, being immune to three types and only being weak to Fire and Ground.
Fighting/Ghost would make for a nice (if frail) offensive Pokemon.
Bug/Psychic would be interesting in another way (although it was have six weaknesses).