I'm afraid I'm not so good with cheap eats in Boston (if I'm going all the way over there it's usually to eat somewhere special, or else I'm just grabbing a slice of pizza on the way to a concert) but here are some ideas in Cambridge if they find themselves over here.
Fast-food style (no table service)Pinocchio's »
www.pinocchiospizza.net/ (Harvard Square)
Four Burgers »
fourburgers.com/ (Central Square)
Olecito »
olecito.net/ (Inman Square)
Regular restaurant style (w/table service)Trina's Starlite Lounge »
www.trinastarlitelounge.com/ (Inman Square - don't bring kids here, it's a bar atmosphere)
Redbones »
www.redbones.com/ (Davis Square)
The Friendly Toast »
www.thefriendlytoast.net/ (Kendall Square)
Cambridge 1 »
www.cambridge1.us/index.html (Harvard Square)
All Star Sandwich Bar »
allstarsandwichbar.com/ (Inman Square)
If you search Chowhound I'm sure you will find a ton of "Boston cheap eats" threads...