Like everywhere else in the world there are several chains of supermarkets in Maspalomas. The ultimate best one is Spain´s famous Mercadona but unfortunately at this time they are not located in the resort area of Playa del Ingles (they are rather in residential neighborhoods in San Fernando, Meloneras and El Tablero). You can go there if you have a car or by taxi. You can also walk there if you feel like it if you´re close enough. Go there if you have to buy a lot of stuff. Prices and merchandise are pretty awesome. They are open Monday thru Friday from 9am to 9:30pm (until 10pm on Saturday). Unfortunately at this time, they are closed on Sunday.
Near Mercadona San Fernando, also good supermarkets are Lidl (open everyday from 8am to 10pm), HiperDino (everyday from 9am to 10pm) and EuroSpar (mo-sa 8:30am to 10pm, su 8:30 to 3pm). There is also the frozen food store 5 Oceanos (in San Fernando and El Tablero).
In the resort area of Playa del Ingles for small quick purchases, you have much more expensive and small express supermarkets scattered everywhere at pretty much every street corner. It does not really matter which one you go to in that case, pick the one closest to you. By order of least expensive to more expensive those are: Spar, Dino, Broncemar, Unide and Cordillo. They close between 9pm to 10pm depending on the chain. After that you have to rely on the small delis opened until 1-2 am.
If you live in Gran Canaria and you have a car, then the huge hyper Carrefour in Vecindario (and Las Palmas) and Alcampo (Auchan) in Telde are also great options for big shopping.