MytiBurger or Roznovskys (sp?) in the Oak Forest area are both delicious! Also Lunch At Sam's on gessner north of Clay is a great place for a well made burger!
HubCap Grill on Prairie(?) about a block east of Main. Smaller than a hole in the wall, very little seating, cash only. You pay for a great hamburger, not the service.
Market Square Bar and Grill....great place for a barley pop as well. On Travis, north of Preston, across from the Market Square park.
Another vote for Christians, but you have to go to the original at Westcott & I-10, not the midtown location. Also, Lankford Grocery is stellar. Hubcap was a let down to me. I really don't want to do this as it will increase the already too large crowd at my local, but Petrol Station has a top-3 burger and a great selection of craft beers (especially if you love hops). The Rancor burger is awesome.