And to close this out with my interpretation of the answer
...
Code:
response.write "<input type='text' name='name1' value='" & RS("PetName") & "' />"
Failed with values having an apostrophe because an apostrophe effectively closes the value='' string (value='John O'Shea')
Code:
response.write "<input type='text' name='name1' value=" & RS("PetName") & " />"
Failed with results with spaces because the value part has no container ("") so will automatically only accept a single word. And now here's the proper solution. 
Code:
response.write "<input type=""text"" name=""name1"" value=""" & RS("PetName") & """ />"
Putting "" inside a VBScript string tells the code to write a single " character.
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