Based on information from:
Sandy/Ivy: per cycle, 2 loads, or 1 load and 1 store. 256bit loads and stores count double, but only with respect to the load or store itself - it still only has one address so the AGU becomes available again the next cycle. By mixing in some 256b operations you can still get 2x 128b loads and 1x 128b store per cycle.
Haswell/Broadwell: 2 loads and a store, and 256bit loads/stores don't count double. Port 7 (store AGU) can only handle simple address calculations (base+const, no index), complex cases will go to p2/p3 and compete with loads, simple cases may compete anyway but at least don't have to.
Sky/Kaby: the same as Broadwell
Bulldozer: 2 loads, or 1 load and 1 store. 256bit loads and stores count double.
Jaguar: 1 load or 1 store, and 256bit loads and stores count double. By far the worst one in this list, because it's the only low-power µarch in the list.
Ryzen: 2 loads, or 1 load and 1 store. 256bit loads and stores count double.