You can use css for this. Set a background-image.
<input type="text" style="background-image: url(/Content/Icons/16/address_book.png);"/>
If you want a small image at the left side (like a search icon for a search box) then add a no-repeat and some padding to make the text be placed beside the image. (in this example I've used a 16x16px image)
<input type="text" style="background-image: url(/Content/Icons/16/address_book.png); background-repeat: no-repeat; padding-left: 16px;"/>
Now you will have a nice textbox with a background icon and the text will not be placed over the icon.