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This is an enhanced version of the code in the answer of Leonid Shifrin. You can specify a starting and ending line number and a CSV/TSV type option for a text file with rows ending with a newline. Notice also the CharacterEncoding option of ImportString that allows to display correctly UTF characters.

ClearAll[impRows];
Options[impRows] = {type -> "CSV", start -> 0, end -> 1};
impRows[fname_String, OptionsPattern[]] := Module[
   {result, ftype, startLine, endLine, strm, lines},
   startLine = OptionValue[start]; endLine = OptionValue[end]; 
   ftype = OptionValue[type];

   (* Open the file stream *)
   strm = OpenRead[fname];

   (* Skip a number of lines in the file *)
   Skip[strm, String, startLine];

   (* Read each line terminated by a newline as a String *)
   lines = ReadList[strm, "String", endLine - startLine];

   (* Close the stream *)
   Close[strm];
 
   result = ImportString[
      StringJoin[Riffle[lines, "\n"]], 
      ftype, 
      CharacterEncoding -> "UTF-8"]
]

I am planning to include this in my DBAPI project together with another extremely useful piece of code for counting lines that I found here. Corrections, ideas, or further enhancements are most welcome.