The fastest the Enterprise in ST:TNG ever went was Warp 9.65 during "Q-Who"- though the ship was still accelerating and probably ended up in the Warp 9.8 range.
In "All Good Things", the three engined Enterprise-D was apparently capable of Warp 13 as that is the speed Admiral Riker ordered after the battle with the Klingons.
So presumably that was quite fast.
But.
The U.S.S Pasteur was capable of Warp 13 as well. Captain Crusher ordered that speed when leaving for the area near the anomaly.
And the Pasteur didn't look like it was a real speed burner.
So how fast could the Enterprise-D go in all likelihood?
Okay, my take on the matter... trying to tie all the TOS and TNG and VOY stuff together...
1) Original FTL propulsion was not warp drive at all. It was subspace-assisted impulse drive. This would be limited to roughly 75c, or approximately what would be WF4.2 (old scale). Zephram Cochrane developed the first "space warp generation" technology, but that was associated with the generation of this sort of "static subspace bubble," not of what we later come to know as "warp drive."
2) A mishap with the subspace generation system leads to the inadvertent discovery of "warp" technology. This is rapidly transformed into a controllable propulsion system, something like 20 years before the arrival of Enterprise at Talos IV. This form of "warp drive" does not use "rippling" interactions between multiple overlapping fields, however... it more closely resembles a misshapen bubble, which the fabric of space-time presses against in an attempt to go to the lowest energy state, providing propulsion.
This form of "warp drive" is pretty much harmless to the space-time continuum, and warp velocities are based upon a pretty simple equation - WF^3 * c.
3) A new breakthrough in propulsion occurs at some point before the refitting of Enterprise. It uses multiple field generators operating sequentially to create the "rippling" but still closed field that gives far more efficient propulsion. This is initially treated the same as the earlier generation of warp drive, and speeds are calculated according to the same scale, but similar outputs of energy can produce much higher effective speeds.
4) The next attempt at an FTL breakthrough is the "transwarp" concept, where you essentially create a 2nd-generation warp drive field WITHIN another static subspace bubble. This is what the Excelsior had, and the "first generation bubble" was created in the big spinal "lump" while the nacelles created the motive power. This would produce velocities, for the same basic power output, of WF^5 * c.
However, there were stability issues and this was never completely successful. Other people attempted "spinoff" variations of this later, also calling them "transwarp," but they're not the same thing
(that's the only way I can justify not just flushing Voyager's nonsensical definition!)
5) In the meantime, another breakthrough was achieved, and as a result, all the "transwarp" work was abandoned in favor of the new system.
Basically, at some point, someone attempted to increase the power of the coil fields, and the "bubbles" begin to ... burst? And you have these big, open field lines (rather than enclosed space-time bubbles) which allow the ships to operate even faster. This gives us the TNG "revised scale" warp drive. Due to significantly different physics (and associated math involved), the scale is "recalibrated," so that (as - unfortunately officially - Roddenberry required) WF10 is "infinity."
The problem is that this "open-field" warp drive technology has a negative impact on the fabric of space-time. It's this technology - AND ONLY THIS TECHNOLOGY - that's at the center of the "warp environmental damage" nonsense that TNG introduced us to.
Several techniques are tried to alter the current generation of drive technology in order to "fix the problem" (Voyager's "transformers" nacelles, for instance) but ultimately, none are as effective as just going back to the earlier generation of technology.
SO... by the time that the Sovereign-class, and the third-generation Galaxy-class ships are launched, they're using an improved version of the earlier (TMP-era) propulsion system again. OR... maybe the first-generation "Excelsior-experiment" type system?
SO... we know that the future 1701-D in "All Good things" was able to go WF13... well above "infinity" according to the "Revised Roddenberry Scale." Yet this seemed very fast... probably faster than 13^3 * c, or 2,197c. Perhaps it was actually "Excelsior Transwarp" factor 13... or 371,293c.
But we know it wasn't the TNG scale... because nothing is faster than "infinity."
