Inkscape uses the Ghostscript interpreter to import Postscript (.PS), Encapsulated Postscript (.EPS) and Portable Document Format (.PDF) files. Ghostscript is supplied with a utility called 'ps2pdf' which Inkscape uses to open EPS files. The problem occurs when Inkscape cannot find this utility.
This is solved by setting your PATH 'Environmental Variable' to the location of the utility. On Windows, if you installed Ghostscript in C:\Program Files\gs\gs8.64, the utilities Inkscape needs are in C:\Program Files\gs\gs8.64\lib. To add this location to your PATH Environmental Variable (after downloading and installing Ghostscript):
1. Right-click My Computer, then click Properties.
2. Click on the 'Advanced' tab and click the button marked Environment Variables. A new dialog box will come up.
3. In the new dialog box, the lower half contains the heading 'System Variables'. Directly below that are the headings 'Variable' and 'Value'. Scroll down until you see 'Path' under 'Variable'. Click it, then click the 'Edit' button.
4. Another dialog box will pop up with 'Variable Name' and 'Variable Value'. Variable Value should already have some folder locations in it. To add the folder with the Ghostscript utilities, click inside Variable Value and go to the end. Add a semicolon (;)and type the path to the utilities, usually something like C:\Program Files\gs\gs8.64\lib. The actual location will depend on where exactly you installed Ghostscript (C:\Program Files in my case) and what version (8.64 here) you have installed. I'm sure you can figure it out..

5. Open Inkscape and Click File|Open. Click the arrow beside File of Type. You should see Encapsulated PostScript (.eps) listed as an option.
Have Fun.