I have heavy clay and am in a low spot, so parts of the yard hold lots of water in the winter; most springs I don't have to start watering until late May, no matter how dry it is. Things that don't like wet feet in the winter expire quickly here.
Here are things that have survived:
Roses: After wet winters, some tend to have black spot in the spring in the area that holds the most water. Roses that are blackspot prone, like Bourbons, have gotten moved to other areas of the yard.
Salvias: S. "Indigo Spires" does well, but needs extra water in the summer. I have it in shade and sun. One that I had in lots of shade bloomed well, but just died one summer. The others have done fine. S. farinacea does really well, blooming from spring to fall, and has reseeded itself a few times. S. coccinea does well in shade, and reseeds itself all over, though it hasn't moved outside the shady area where I originally planted it. S. guaranitica, the light blue one (Argentine Skies?) has done well and spread by underground runners. The dark blue one, which is really nice, died; I finally quit rooting cuttings because it invariably died in early spring, after the winter rains. S. uliginosa, bog sage, does really well, taking wet feet in winter and surviving droughty conditions both. S. luecantha, Mexican bush sage, does fine as long as the drainage is good. S. darcyi does well and spreads by underground runners; it's a really nice shade of scarlet. S. greggii and S. microphylla have done well for me, but I am careful to put them in more sun than shade and to put them where drainage is as good as it gets in my yard. S. mexicana and S. madrensis have to be carefully sited, with excellent winter drainage to make it here. The bicolor sage, whose Latin name I've forgotten, S. regla, S. iodantha, S. karwinski, S. jamensis, and all the S. greggii and S. microphylla crosses that are bicolor or are purplish have died here; they don't like winter rain.
Natives: These all do well in my clay soil: American beautyberry, Mexican buckeye, red buckeye, coralberry, Carolina buckthorn, native passionvine, Carolina jessamine, yaupon, possumhaw, Gulf muhly, Lindheimer's muhly, verbena hastata, rough-leafed dogwood, anachaco orchid tree, kidneywood, salvia ballotaeflora, salvia engelmannii, lantana horrida if given good drainage, redbud, Texas redbud, Mexican plum, thicketing plum, coralbean, coastal live oak, liatris if given good drainage, aromatic sumac, prairie flame-leafed sumac, beebrush, wax myrtle, cherry laurel, rusty blackhaw viburnum, native honeysuckle bush and vine, both, desert willow, zexmenia, and turk's cap. Surprisingly, evergreen sumac has done well. That one is supposed to be sensitive to overwatering, and I thought for sure I'd lose it the year we got 50" of rain. It is in a part of the yard that drains better, so maybe that helped. Agarita is barely surviving. I just potted it up, as it looked like it was drowning in the bed where I have it. If it lives, I will move it to a better draining bed. Maximillian sunflowers get really big and floppy here when there's lots of rain. I do not water them much during droughts, maybe once or twice a summer. Otherwise, they are floppy. Natives that I wish didn't do so well here: poison ivy, peppervine, wild grapes, grass burrs, widow's tears (dayflower), dewberries. Flame acanthus has struggled with the clay soil, but not expired yet. Lindheimer's senna died a slow death; it just couldn't take the wet winter/clay soil combination. Mexican bird of paradise died to the ground in the year that we got 50 inches of rain, but resprouted from the base and is still alive.
Other things that have done well: leatherleaf mahonia, a very slow grower, some type of low, gray cotoneaster, Mexican oregano, Mexican honeysuckle, gold lantana, lantana camera, pomegranate, dwarf pomegranate, flowering quince, nandina, some type of small holly, and spirea.