How many? Why not count? :-)
Take the total number of menu items, numerical digits, adjustable ranges, etc. in your entire UI. Call this (options).
Estimate the time you want a user to spend faffing around in the menus, navigating to the thing they're trying to find (hopefully only a few seconds, even for the most obscure settings*). Divide this time by the average amount of time taken to find and press a button (~0.5s?). The result is the number of button presses you expect the user to enter, to get somewhere. Call this Np.
The amount of information conveyed by X button presses, selected from B buttons, is B^Np combinations. Maximum. So to get (options) = B^Np, you need B = (options)^(1/Np). Minimum.
*If your options have differing frequency of use, that implies you can save keystrokes, in the average case, by assigning priorities to them. On a side note, voila -- you now understand Huffman coding (as used in e.g. JPEG files)!
A home thermostat might have menus countable on one hand, and total options countable on several. You only need a few buttons. Up and down are priority for a small-range numerical input, then you might add one more enter/escape/magic/more-magic button. Expect ~0.5s per button press, and total interaction of 1-2s. Menu naviation might be by menu item ("go back" item) or shortcut.
An oscilloscope might have dozens of menus, totalling hundreds, even thousands of options. The large number of numerical inputs (plus the historical influence of knobs on scopes) demands rotating inputs as well. I count 35 buttons and six encoders on my scope. It still doesn't feel like enough inputs, but that's Tek's fault for committing the number one mortal sin: the interface responds considerably slower than (average_time_to_find_and_press_button). The whole UI team should've been fired for that!
Indeed, the sheer dynamic range of some options makes not only bare encoders laughable, but demands adjustable-decimal-place entry. Which is a feature rarely supplied on scopes, yet so sorely needed! Compare to most function generators, which have all digits accessible for the frequency setting.
Tim