Due to history, Serbia has a mixed cuisine - the austrian and hungarian influences from the north, the turkish and other oriental from the south. Add the minorities and neighbors and their cuisines and you get an incredible mix.
So on the one end, there are the šampita (foam pie, of sugar-stiffened cream, thin layer of pastry on the bottom, of chocolate on top, about 10cm tall), krempita (similar but not as sweet, pastry on top and bottom, yellow egg-milk-sugar filling between, about 4cm tall), kiflice (small crescent rolls with bit of pekmez (qv at winter preserves) inside, derived from german kipfel or some such), krofne (from krapfe, fried spoonful of dough which blows up to a tennis ball size), princes krofne, lazy pie (two layers of dough, pekmez of sour cherries or grated apples or poppy seed layer in between, dusted with powder sugar). Then, further down the norhtern lane, without description: kuglov, buhtle, pajgle, pišinger, rolat, koh, puslice, various štanglice, bajadera, šufnudle and other words of german origins.
Then there's a whole series of things done with filo dough, which you can buy pretty much anywhere or in specialized workshops. As far as one generation ago, any homemaker would proud herself of making her own filo dough, spreading it in an expanding circle all over a table, lining up the fill (same as for lazy pie, or also pumpkin, young cheese, or ground meat or even potatoes and onion - though that's not a cake then, but a regular meal) then lifting up one side of the tablecloth to make a long roll. That roll would be zigzagged or spiraled into a pan and baked in the oven. That's savijača (bender or roller), but there are also česnica, a rich ritual cake with lots of walnuts and honey, which is served on christmas with a coin hidden somewhere inside. Whoever gets to eat the piece with the coin, is nominated the (honorary) boss of the family for the year, which is usually forgotten the next day. There's also a vasiljica, made for yet another january holiday (yes, christmas is on 7th of january, the Serbian orthodox church still holds to julian calendar), pretty much the same just not as rich - fewer layers, less honey.
There's also a different rolled cake, štrudla (yes, the strudel), which you can also buy vaccum packed in many supermarket - with sour cherries or poppy seeds.
Going more south with the cuisine, more filo dough: baklava, of greek origin, almost the same as česnica except it's not layered with honey, but rather doused in very sugary solution, so it's soft (and you need a little fork - most of the above you can eat from your hand).
And then there are the torta (equivalent to tart or birthday cake) which are regularly layered, cover the whole plate, between each layer of dough there's one layer of fil (i.e. filling :), and then it may all be covered with a different kind of fil, optionally decorated with grated chocolate, whipped cream patterns etc. There are many known recipes, and many a homemaker has a whole stack of them. The most popular seem to be the doboš torta (drum cake) and reform torta (nobody knows which reform and of what).
Note that the word for cakeshop is "poslastičarnica", and they generally have their own ice-cream, lemonade (from real lemons, or at least used to be so), and make at least a quarter of items from the above list. Don't go for čiskejk (cheesecake) and fancy big places with names in english at good locations, they're in it for the money and you may get a kesten pire (chestnut puree) which doesn't taste like chestnuts at all, or cheesecake made with yogurt and cream cheese and whatnot. Go for the small ones, where the name of the owner is up front.