I wrote:

"I'd have to think about the others."

Well, I have, and my conclusion is that they are all common, except for IV 7, but one could probably find this one, too.

I7 --- Resolves to IV or iv (C7 --> F maj/min)

II7 --- Resolves to V or v (D7 --> G maj/min)

III7 --- Resolves to vi or VI (E7 --> A min/maj)

IV7 --- Resolves to bvii or bVII (F7 --> Bb min/maj). This is the only one that resolves to a chord with a root outside of the key. Is therefore a quick and painless way of modulating a whole-step downwards. However, iv (e.g., Fm in the key of C) is quite common.

V7 --- The dominant of the key. Can't get more common than that.

VI7 --- Resolves to ii or II (A7 --> D min/maj)

VII7 --- Resolves to iii or III (B7 --> E min/maj)