Biggest was Iconian empire ~200 000 years ago; it spanned the entire galaxy not including a few systems on the very outer rim (stealing lingo from Star Wars). The empire spanned from Iconia in the far stretches of the alpha quadrant near Orion space in the RNZ, to Vandros IV on the other edge of the Gamma quadrant (DS9 "To The Death"), to Vaduaar Prime in the Delta quadrant. There were few corners of the galaxy they didn't control. They were the most successful empire due to their stupendously advanced gateway technology that completely eliminated the need for starships of any kind(TNG "Contagion").
2nd was the T'kon empire, ~600,000 years before present, which spanned most of the alpha and beta quadrant. Their gravitational energy field technology (first, and only seen in TNG) allowed them to move planets and stars, and is the reason they got to #2 for empire size (TNG "The Last Outpost").
3rd is Borg, who control most of the Delta quadrant, expect for Kobali and Voth space, the only species in the Delta quadrant who have been successful in 'sharing' a quadrant with the Borg.
4th is the Dominion, who are the undisputed top dogs of the Gamma quadrant; however, they are not in control of the entire quadrant.
5th is the Federation, who control a good chunk of the Alpha quadrant, and if you count Star Trek Online lore, then in 2409 they amalgamated the Cardassian and Bajoran space into their own.
As for the rest ; Klingons controlled a good amount of space, especially if you count STO lore. Romulans same, about 70% the size of Klingon space. Other than that, who tf cares.
If you don't restrict this to OUR galaxy...
1 without a doubt is the Kelvan empire, who control the entirety of the Andromeda galaxy and have fast enough ships that they colonize other galaxies, and made contact with Kirk's enterprise before he told them to F*** off out of the Milky way (TOS "By Any Other Name").
2 would still be Iconian.
3 would be the Undine (known by their borg designation: species 8472) who appeared in (VOY "Scorpion p1&2"). Their reign lies in fluidic space, but B'elanna Torres theorizes by preliminary scans that their empire is not quite, but close to the size of our galaxy.