How much? If the mechanical trimmer were perfectly accurate and consistent (it isn't), adding 38 pixels to the total width of your image would work. We recommend you allow 0.25 inches (75 pixels) on an 8x10 print to fully allow for worst cases.
SmugMug recommends you keep bleed/trim in mind for all print sizes, even those big enough to print on a different printer.
What if you can't lose any of your print? Use Photoshop's Canvas Size command (not Image Size) to add at least 38 pixels to the width and height. They should be pixels you can lose but won't show badly if a few get left by the trimmer.
Should I Worry?
In general, we only see problems in three specific cases:
Montages. The above example elegantly avoids possible bleed/trim issues.
A very closely cropped picture where every pixel is critical. If the photo below left was printed as is ...
... losing just 5 pixels from the top means we've lost the baby's toe! To the finicky customer, this means a reprint or refund.
Images with text very close to the side. If the photo below left was printed as is ...
... it's quite possible a 3 pixel loss would obscure the name. Almost any customer would require a refund or reprint in this case.