Automatically add appropriate prefix to Quantity

EDITED to include Mr.Wizard's replacement for Switch EDITED to cover additional cases

Roll your own:

quantityWithAppropriatePrefix[quant_Quantity] := 
  Fold[UnitConvert[#1, #2] &, quant,
   {"Imperial", "SI"}];

EDIT: As Kuba pointed out in a comment, this can be written more compactly as

quantityWithAppropriatePrefix[quant_Quantity] := 
  Fold[UnitConvert, quant, {"Imperial", "SI"}];

quantityWithAppropriatePrefix /@
 {Quantity[0.0000011, "Meter"],
  Quantity[0.0000033, "Feet"]}

{Quantity[1.1, "Micrometers"], Quantity[1.00584, "Micrometers"]}

A brute force approach:

quantityWithAppropriatePrefix[quant_Quantity] :=
 Module[{si = UnitConvert[quant, "SI"], mag,
   log10Mag, multiplier},
  mag = QuantityMagnitude[si];
  log10Mag = Round[Log10[mag], 3];
  multiplier = {"Yocto", "Zepto", "Atto", "Femto",
     "Pico", "Nano", "Micro", "Milli", "", "kilo",
     "Mega", "Giga", "Tera", "Peta", "Exa", "Zetta",
     "Yatta"}[[log10Mag/3 + 9]];
  Quantity[mag 10^-log10Mag, multiplier <> QuantityUnit[si]]];

  quantityWithAppropriatePrefix /@ {Quantity[0.0000011, "Meter"], 
      Quantity[0.0000033, "Feet"]}

{Quantity[1.1, "Micrometers"], Quantity[1.00584, "Micrometers"]}

Partition[Table[quantityWithAppropriatePrefix[
    Quantity[1.23*10^n, "Volt"]], {n, -25, 25}],
  6] // Grid

Just a variant:

qf[u_] := Module[{rng = Range[-24, 24, 3],
   multiplier = {"Yocto", "Zepto", "Atto", "Femto", "Pico", "Nano", 
     "Micro", "Milli", "", "Kilo", "Mega", "Giga", "Tera", "Peta", 
     "Exa", "Zetta", "Yatta"}, v, p}, 
  v = QuantityMagnitude[u];
  p = First@Nearest[rng, Log10[v]];
  Quantity[
   v 10^-p, (p /. Thread[rng -> multiplier]) <> QuantityUnit[u]]
  ]

This is a brute force solution, but seems to be more robust and does not require an internet connection, that I put together based on the other posts in this thread.

AutoSIPrefix[quant_Quantity] := (Module[
    {prefixlist, prefixrules, siunitstring, pfloc, baseunit, 
     basequantity, mag, log10Mag, prefix, newunit},
    prefixlist = 
     "kilo" | "mega" | "giga" | "tera" | "peta" | "exa" | "zetta" | 
      "yotta" | "deci" | "centi" | "milli" | "micro" | "nano" | 
      "pico" | "femto" | "atto" | "zepto" | "yocto";
    prefixrules = {3 -> "Kilo", 6 -> "Mega", 9 -> "Giga", 
      12 -> "Tera", 15 -> "Peta", 18 -> "Exa", 21 -> "Zetta", 
      24 -> "Yotta", -1 -> "Deci", -2 -> "Centi", -3 -> "Milli", -6 ->
        "Micro", -9 -> "Nano", -12 -> "Pico", -15 -> 
       "Femto" - 18 -> "Atto", -21 -> "Zepto", -24 -> "Yocto", 
      0 -> ""};
    siunitstring = QuantityUnit[UnitConvert[quant, "SI"]];
    pfloc = 
     StringPosition[siunitstring, prefixlist, IgnoreCase -> True];
    baseunit = 
     If[Length[pfloc] == 1, 
      Capitalize[StringDrop[siunitstring, pfloc[[1]]]], 
      Capitalize[siunitstring]];
    basequantity = 
     UnitConvert[quant, 
      Capitalize[StringDrop[siunitstring, pfloc[[1]]]]];
    mag = QuantityMagnitude[basequantity];
    log10Mag = Round[Log10[mag], 3];
    prefix = log10Mag /. prefixrules;
    newunit = Capitalize[ prefix <> ToLowerCase[baseunit]];
    UnitConvert[quant, newunit]]);