One of the running gags in Bob's Burgers is the burger of the day. The burger of the day is a special burger that the restaurant makes every day. Each burger of the day is a pun. (Almost) every episode has a burger of the day pun at least in the background. Another running joke is how Louise will sneakily change the Burger Of The Day to a (usually) very inappropriate pun (like her burger of the day "The Child Molestor" as shown above).
To the right of Bob's Burgers is a constantly changing store. This store is a running gag, as each episode it changes to a new store with a pun in it's title.
The Pest Control Truck is a gag that happens in the show's opening. A new pest control truck is shown in each episode, with a different pun in the truck's comapny's name.