Some of my favourites would be Sonic X and the Tales of Anime adaptations. Still holding out hope that the Crestoria manga gets adapted into an anime, that story was way too good to be doomed to a defunct gacha game.
The Xenosaga anime is middling, which is a shame because the Xeno- games are easily some of my favourites. I wouldnt mind if monolithsoft revisited the series with one of their newer Xeno games, xb1 in particular I think would make for a really good anime if left in the right hands. Or maybe if one of their other series got an adaptation...
Final Fantasy Unlimited is one that really deserved a better shot, genuinely a great premise that was abandoned at the altar. If you want to count Spirit Within and Kingsglaive then they sucked, I guess. I liked Advent Children Complete though. And while I'm at it, Kingdom Hearts X Back Cover probably doesnt count, but even still it bored me to sleep watching it. Square kinda sucks at adapting their franchises into anime, their manga is a different story altogether.
Fate/ is one that people seem to forget is adapted from a game series because most people are exposed to it through the anime. I think the fate games are pretty good, and I havent played Samurai Remnant yet that looks to be pretty fun. I think Fate/Extra and the Extella games are ok, but if Fate/Extra Record actually releases (pretty sure the game is cancelled) then I'll probably regard that as the new favourite.