I usually bring the panniers into the supermarket in order to have something to pack the shopping into. That said, I do occasionally leave one pannier with nothing in it (well, maybe a couple of bungees and an inner tube) attached to the bike when visiting shops that don't have trolleys, so as not to have my hands full.
My tools and pump[1] live in the pannier, so I don't have to worry about them. Dynamo lights mean they stay on the bike. Years ago I realised that the chances of someone nicking a bike computer were vanishingly small compared to the chances of me dropping one while wandering round a shop, so that stays attached too.
This has reminded me of a folding bike (Dahon shaped object) I saw last week secured by wrapping it round a signpost, with no obvious sign of any lock. I suppose it might slow them down.
[1] The no longer made Cyclaire Plus is ideal for this, as it has a box-shaped bag with a pocket for your puncture kit, rather than being an awkward long thin thing.