If you have slept well, you might say that you have slept like a baby, like a log, like a rock, like a top or like a lamb. Apparently in Chaucer’s time you might have said that you had slept like a swine, or whatever that was in Middle English [source].
If you search for “sleeping” on Flickr, as I just did, you mainly get photos of sleeping cats and sleeping babys, so maybe you could also say that you slept like a cat. The cat in the photo above is my sister’s cat Fletcher, by the way.
In Welsh you might sleep like a hog / wild boar (cysgu fel twrch), or like a hedge (fel clawdd), like a sow (fel hwch), like a pig (fel mochyn), like a small rope/cord (fel cordyn), like a nail (fel hoelen), like a stone (fel carreg) or like a mole (fel gwadd) [source].
In Scottish Gaelic you could say bha cadal nam maigheach orm (I slept like a hare), and cadal nam maigheach ort!, or literally “sleep of the hare on you”, is how you say “sweet dreams, sleep tight!” or something similar [source].
In French you might sleep like a dormouse (dormir comme un loir), like a marmot (comme une marmotte), like a stump (comme une soche), like a baby (comme un bébé) or with closed fists (à poings fermés) [source].
What about in other languages?
