First there was Neo-Geo Pocket.
Not too long after, SFA3 Upper on GBA assumed the portable fighting game throne.
Then, Tekken 5 and Soul Calibur on PSP rocketed the whole genre to new heights on handhelds.
UMvC3 gave us a glimpse of what could now be possible, and DOA5+ looks poised to bust through that door and deliver the future today (or on Tuesday, whatever).
Bow down before Team DOA, your new gods.
Revised-
First, there were the Takara SD fighters on Gameboy, which got good after World Heroes 2 JET came out. Props to Fatal Fury Special on Game Gear too.
Then there was the Neo-Geo Pocket which was pretty much perfect for the time.
The GBA got it right with SFA3 Upper and KOF EX2.
PSP continued the awesome with Darkstalkers, more SFA3, Tekken, and Soul Calibur. Unofficially, near-perfection was achieved with emulation.
DS had...uh...well Bleach DS2 was OK and had online!
The 3DS brought several games with good online play, although network functions were limited.
Then the Vita brought near-perfect versions of fighting games to portables. Street Fighter X Tekken set a new standard with cross-buy DLC, cross-save (for certain settings), and cross-play. PS All-Stars followed in its footsteps and offered cross-buy for the game.
DOA5+ looks to take SFxTK's crown and improves on the save system, but may falter due to the lack of lobbies and the removed tag system. Even then it still looks to be an excellent port.