In Polish:
sit — siad!
heel/here — noga/do nogi! (lit. "leg/to the leg!"), chodź! ("come"), do mnie! ("to me")
bark — daj głos! (lit. "give voice"; we do have a separate word for barking too, though!)
lie down — leżeć!
stop — stój!, stop!
roll — turlaj się!
stay — waruj! (for staying while lying down, traditionally used with guarding in mind), zostań!
attack — never really heard anyone using it, but I guess it would be atak/atakuj!
guard — pilnuj!, waruj!
jump — skacz!, hop!
search — szukaj!
fetch — przynieś!, aport! (when playing fetch)
leave it/no — oddaj/puść! (for objects held in mouth), zostaw! (a more general "leave it"), fe/fu/fuj/ble! ("yuck!"), nie! ("no!"), stop/przestań! ("stop!")
give your paw — (po)daj łapę/łapa! ("give [your] paw"/"paw!")
go (ending the command) — various may be used, f.e. okej/dobra ("okay")
praising the dog — świetnie/dobrze! ("great"/"good!"), super!, brawo!, dobry pies! ("good dog!")
play dead — zdechły pies/zdechł pies! ("dead dog"/"the dog died!")
For horses:
prrt! ("stop/hold on!"), wio! ("go on/faster!", wiśta wio! is a more energetic version, should you get in spirit)
Calling animals:
cats — kici-kici, pspsps
chickens, some other birds — cip, cip!
ducks — taś, taś!
rabbits and most rodents — the sound of clicking your tongue against the alveolar ridge
squirrels — Basia/Baśka! (a Polish diminutive of the name Barbara; honestly, I have no idea why we call them so, but my grandma says they respond to it, so who knows... ;>)
a bit oddly, we don't have a specific call for dogs besides a whistle.