Well, quite obviously there are instruments that do not have overlapping ranges, which is kind of the idea behind having different ranges. To make Mr. Phoog happy here is an example of such: The highest instrument of the typical symphonic orchestra is the piccolo flute, which cannot go lower than a C5. The lowest common instrument would the contrabassoon, whose range is usually considered to go up to C4.
Of course possible way to counter this is by transposing in octaves. This does make a lot of sense as with a change in register you also get changes of colour, dynamic expressibility and such. While it would technically be possible to play a piccolo part on the bass tuba it will not sound good together. Or more reasonably: The bass clarinet can play a lot of clarinet stuff in the original octave, but it will sound differently.
If we were to talk about the individual ranges it is quite safe to assume that most professional instruments have at least a range of 2-2.5 octaves. Of course this then depends: There are instruments such as percussive instruments and keyboard instruments that do have a very specific set of pitches. You do have string instruments where the range is limited above by the length of the fingerboard (although technically you can do harmonics to get more range upwards). You get brass instrument where the range is limited by above only by what you can achieve on your mouthpiece using lip tension. And there are woodwinds, where the upper limits depends on how many overtones you can overblow.
So while brass and woodwinds theoretically do have no upper limits, going higher on these instruments gets really hard quickly. (Also strings do have not theoretical upper limit, using harmonics.)
So we see that most instruments do have a hard lower limit and some sort of soft upper limit, which can be pushed up by technique. This means that technically this "shared range" is only limited by the instrument with the highest lower limit, which would be piccolo. But this is not really reasonable.