Not whales, seahorses or lobsters I'm afraid.
Gannets, swans, geese and some other animals do have apparently exclusive partnerships which go on from year to year -- perhaps even till death do them part. Not sure about magpies (how would one tell -- they all look the same!)
However, in some cases it's just for show. DNA testing of offspring has shown that many apparently monogamous animals are actually carrying secretly on with someone else. A male bluetit, robin or what have you will sing loudly from a tree top in his own territory and look like a committed "new bird" -- but then will quietly slip into a bush with next door's hen...
A lot of research has been done into the "game theory" of this -- working out what strategy leads to the best chance for one's offspring and genes under different conditions. Mass orgy like a herring, careful monogamy like a gibbon, or serial brief pairing like a pheasant?