It's not really a remake, but Gradius Rebirth is the shit.
Don't forget Contra Rebirth.
The Castlevania Adventure Rebirth on the other hand is more meh given the lazy mishmash of spritework and cribbing from several of the 16-bit era Castlevania games. Then again, its a hell of a lot better than the original version.
Edit: Does the GBA count as 16-bit given the GBA's level of technology and not the period of time it existed? If so then
this may eventually be relevant given the fact that it was probably the single best series to grace the GBA (outside of Fire Emblem).