Well, humans were dreaming of building warp 7 ships as of "TATV". One wonders if anything ever came out of it.
Is Kirk's ship a warp 7 vessel, say? Scotty gets a cardiac arrest every time Kirk orders a speed higher than warp 6... OTOH, it seems that any ship can reach arbitrarily high speeds with sufficiently many people sitting on the safety valve - this merely shortens the expected lifetime of the ship and the crew to varying degrees.
Archer's ship for some reason never had to suffer the indignity of traveling way faster than the recommended maximum speed. I wonder why? Something inherent in the engines? Or just a general strategy of avoiding tugging Superman's cape?
That reminds me of this little exchange in the "Fallen Hero":
T'POL: Holding at warp four point nine, but Commander Tucker doesn't believe we can sustain it for more than another ten minutes.
TUCKER: Please tell me you're ready to slow down.
ARCHER: Sorry Trip, but we need a little more speed.
TUCKER: I don't know how much more I can give you.
ARCHER: It's called a warp five engine.
TUCKER: On paper