What is the percent impedance of a typical residential power line transformer?
I can't speak to American/ANSI standards, but in Australia we use AS/NZS standard 60076.5-2012 Power Transformers - Ability to withstand short-circuit as a guideline for the absolute minimum impedance of power transformers. Note AS/NZS 60076.5 is equivalent to IEC 60076.5.

Table 1 of that standard gives absolute minimum percent impedances for various transformer sizes. I cannot reproduce the entire table, but the relevant part for you is:

Table 1 - Recognised minimum values of short circuit impedance for
          transformers with two separate windings

          Short circuit impedance at rated current

Rated Power (kVA) | Minimum short circuit impedance (%)
------------------+------------------------------------
   25 - 630       | 4 %
  631 - 1,250     | 5 %
1,251 - 2,500     | 6 %
     ...          | ...


Noting that most residential transformers will be in the 200kVA - 2,500 kVA range. (Pole top transformers can be as large as 500 kVA; past that, up to 2,500 kVA, they tend to be pad-mount on the ground.)



Why are these the typical values?

The reason this information is found in the standard about "ability to withstand short circuit", which is an odd place to find it, is because the transformer impedance is important in limiting the current through the transformer under fault conditions.

A minimum impedance limit implies a upper limit on the through-fault current, hence a limit on the maximum energy dissipation and dynamic force under fault conditions.

The maximum energy dissipation and dynamic forces directly influence the design of the transformer. For instance, AS60076.5 mandates that the transformer must be able to withstand two seconds at maximum through-fault current without sustaining damage from heating, so the conductor thicknesses and so forth must be chosen to accomplish this.

At a guess, the exact values found in Table 1 were chosen because it was found (experimentally) that these were the lowest impedances it was possible to specify, while still having a sufficiently reliable and robust transformer.



Can transformers be ordered with "non standard" impedances?

Transformers can be ordered with a different impedance than the minimum set forth in AS 60076.5, which is only a suggestion. It is common to order transformers with a higher impedance, so the fault levels on the LV system are reduced. I have seen 2,500 kVA transformers ordered with impedance of  12%, which is double the minimum standard impedance, for fault limiting purposes.

It is not common to ask for a transformer with less than the standard impedance, as such a transformer will have a very high LV fault level, which is bad for equipment and personnel safety. Additionally, the high fault level will tend to make the transformer self-destruct under fault. As such, transformers with less than minimum impedance would only be ordered if you really knew what you were doing, and you were willing to waive some of the fault-withstand requirements set forth in AS60076.5.