We do:
Tesco... nearest, but local one isn't huge. OK, nothing to paricularly write home about, but not bad either.
Sainsbury's... most of the time. By default really as ds1 one does an activity nearby which means I've got to be there for an hour twice a week anyway.
Lidl...buy selectively, not for a full shop: good for pesto, continental deli meats, decent but inexpensive orange juice, part baked walnut bread/ciabatta, chocolate, frozn goose, german sausage, continental Christmas foods (leberkuchen, gluhwein, etc). Often get Waitrose shoppers saying "ooh where did you get ?" to Lidl items!
Aldi...see Lidl - but isn't very local so don't use it often.
Waitrose... occasionally (bit of a pain to get to as it's in a town I'm not usually stopping/shopping in) - good for an intersting selection of cheeses, or something different for a special meal.
Morrisions... good for bread, sausage rolls, fish, real Wensleydale, frozen baby sweetcorn (can't find that anywhere else).
M&S - too expensive for regular use. Occasionally splash out on the meal for £10 deal.
Iceland - occasionally if we're catering for an event (frozen bhajis are good) and need to bulk buy.
Makro - used to be good for bulk buys/more restauranty desserts but they closed the local one
Asda....rarely. Never entirely convinced by the quality of non-branded things, and always has horrendous queues for the tills.
Farmfoods... good for stocking freezer with standby frozen veg the others don't have. Local one got taken over by M&S and closed though.