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?FileExistsQ, 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](http://healis.eu/dbapi/) together with another extremely useful piece of code for **counting lines** that I found [here](http://mathematica.stackexchange.com/questions/23499/determine-the-number-of-lines-in-a-text-file). Corrections, ideas, or further enhancements are most welcome.