What do animals do in their spare time?

It sounds rather silly, but in our case at least, once we developed agriculture, we could afford having people pursuing other pastimes, perfecting and creating a culture of specialists and driving our cultural evolution. Now, I'm not implying anythig like that happening anywhere else in the animal kingdom, but animals that live in food abundant habitats - think urban areas!, like pigeons in parks that don't have to spend their days searching for food since everyone feeds them, surely living off another species should create an excess of free time, so how did the human presence affected their way of life, daily routine, what do they do with the time they would've otherwise spent searching for food? Do they make more complex nests? Spend more time with their young? Did their behaviour change in any way?

What an interesting question!

My first thought is that most don't really have spare time since they still tend to be foraging.  So taking your pigeon example (or think about rats, urban foxes, ducks on ponds, many other species) the abundance of food provided by humans (intentionally or not) results in greater survival to reproduction, and more babies being produced (which could take up more time as well). Bigger populations collectively consume more resource - so to some extent the ecology takes care of the situation. More food will mean more individuals competing for it.

Of course, many animals that aren't actively foraging ('downtime', so to speak) spend time either grooming to remove ectoparasites (all mammals and birds) or, if they are a social animal, engaging in social activities (which may also include grooming, or even recreational sex, if you are a bonobo!). If you're young, play is often a very large part of the day too and some adults from some species will also engage in this with their offspring and that of others.

Some species spend a lot of time sleeping (think lions, bats etc.) or simply ruminating (cows etc.) / digesting (foliverous monkeys, like howlers), if you have a cellulose heavy diet.