Decided to place my favourites in each victory type (and a flavour civ):
1. Scotland - scientific victory; like the emphasis on happiness, I also enjoy closely packed cities and the cool production bonus, the UU doesn't do much, though. Oh, and the great scientists and engineers are always useful.
2. Mongolia - domination victory; Mongolia takes some early-game planning to fully shine, it is not just a brain-dead horse-spamming civ. The extra movement and the escort ability makes it hard to return to another warmongering civ. UU, although not particularly strong (suffers against walled cities) delivers much flavour, as does the combat strength bonus. It is also super cool to stretch across all of Asia on TSL maps.
3. Persia - cultural victory; I like to switch to cultural route with Persia at the end of the classical era, after waging surprise wars and blitzkrieging my enemies with those speedy Immortals (please, make the take cities again). The extra gold makes it more forgiving to focus culture instead of science and gives an option to patronage GP if needed.
4. Khmer - religious victory; I can't get over the unique mechanics of this civ. Sending missionaries to death to grab myself boosted relics and pursuing both cultural and religious victory. Larger cities mean more science and culture while being somehow supported by amenity bonuses. The only problem is the early religion spread - you need to be fast, as other religious civs are almost guaranteed to have more faith than you thanks to more optimal holy site positioning. Domrey is a destructive unit, although an expensive one.
5. Poland - flavour civ; decided to put Poland over Rome. Poland can take many routes, the most optimal being warmongering religious one. Finding the first religion is quite easy with wildcard policy slot. After ensuring Crusade belief, culture bomb your opponents and strike the newly-believing cities with a deadly charge of winged warriors. Take as many cities as you want, convert all of them while also sending missionaries and apostles while in a golden age to players currently at piece with. Finally, use your acquired cities of the Polish Empire in a trade deal to the always present hard-to-convert AI and enjoy one of the earliest victories.