okay, this should be taken to the casual discussion, but I'll put my word in on it.
DOA is what basically created the modern online fighter back with 2u. Before that fighters were very few and far in between, then DOA4 was like, the ONLY Online fighter for the longest time.
Since DOA4 we've had other online fighters come in, and none of them did anything to be influential, really.
We got SF4, which was just SF again, nothing influential from that other than the rabid fanbase. (Though SF4 desperately tried to pretend that charge moves were something new lol.)
We got Soul Calibur/Tekken, which did do the character creator/customization, so I give it that.
Then we got all the flashy anime spazz seizure fighters like MvC3/Skullgirls/Blazblu/P4A, which also added nothing, so no influence there, since they were just rehashes/sequels to older fighters MVC2 and GG.
Then what we have besides that is the arena/anime fighters, like DBZ/Naruto/Jojo. DBZ has been getting shallower since Raging Blast, losing any influence it might have had, Naruto is all about the visuals, not the mechanics, and I haven't played JoJo yet, but seems to be in the same boat as Naruto.
Then Mortal Kombat had the great story mode cutscenes, though that's hampered by the story itself sucking bad. And the fact that the actual Kombat was as hilariously stiff as ever.
Looking back at all the big name fighters of the past 10 years or so...DOA4 was the most influential. It was the only real ongoing fighting series, basically kickstarted online fighters, real environmental hazards, was THE online fighter for the LONGEST time, still the most fluid fighter, etc.
Only "influences" from others would be
SF4 - More remix editions that unfortunately is a trend DOA5 is taking after
SC/Tekken - Character customization. Which was actually bad because it wound up just being constant cosplays.
and that's about it.