It seems like every country has its own signature sweet anise-flavored liqueur. A non-exhaustive list:
Italy: Sambuca
France: Absinthe
Greece: Ouzo
Germany: Jagermeister
Bulgaria: Mastika
Columbia: Aguardiente
Turkey: raki
Middle East (many countries): Arak
Which ones are the best? How do you like to drink them? Of the ones I listed, Jager is my favorite, although it’s flavored with many things besides anise.
I drink arak, specifically Arak El Namroud, a Lebanese-style domestic brand distilled in the Galilee. Smooth and tasty, it’s probably my main source of alcohol consumption.
From your list I have tried: Sambuca, Absinthe, Ouzo and Jagermeister. The one we drink most often in the CT_D household is Galliano. I prefer them (and most liqueurs) room temp neat.
Nitpick: it’s “rakı”. Note that the “i” doesn’t have a dot. This gives it a sound which doesn’t really exist in English, but is closer to a “u.”
You could almost split these into two or three groups. Many, like absinthe, pastis, and rakı, are usually expected to be mixed with water. Others, like Jägermeister and Galliano, are more like liqueurs and have other ingredients. I seem to recall that Sambuca is meant to be drunk neat or on the rocks, so it’s a bit unique.
I had Jägermeister recently and it was much more smooth than I remember it. It might help that I am part of that estimated 2% of the US population who can tolerate anise/licorice. But even then, it isn’t as harsh as things like absinthe.
From the list, I’ve tried Sambuca, absinthe, ouzo, and Jägermeister.
Of the last, the less said, the better, perhaps–I find it irredeemably vile.
My experiences with Ouzo have been mixed; it seems to vary quite a bit by brand. Some of it has been very tasty, while others have been a bit insipid.
Sambuca and Absinthe both reside on my liquor shelf: Sambuca to be consumed neat for its clean anise flavor (no coffee beans for me, thank you), and absinthe for occasions when I’m feeling archaic and decide to engage in the proper ritual. 
Try a good US made hand-crafted absinthe such as Chicago’s Sirene or
Seatle’s Pasifique.
http://www.northshoredistillery.com/absinthe.htm
http://www.pacificdistillery.com/
I’d have listed pastis rather than absinthe; while they’re both anise flavored, pastis is a lot nearer the other drinks you’ve listed than absinthe is.
Aguardiente is not always anise flavored; there are regional variations and in many regions flavorless (by which I mean there are no added flavors) is the default.
Yup, I dont know what absinthe stands for exactly these days in France. I think the Spanish absinthe is not that far from the original stuff, I dont think that’s the case of French absinthe.
That said the traditional anise drink of France is pastis. Extremely popular in the south of France. Reasonably popular in the rest of the country, though mostly favored by the older generations.
I’ve had all the ones listed except mastika. They were all irredeemably vile.
That people willingly drink the stuff with regularity is one of the puzzlements of Humanity.
I’ve had all those but Mastika, Raki, & Arak - Sambuca is my favorite. I might have to seek those three out to try them, because I love anise flavored stuff. Yes, the black jellybeans are my favorite kind. I used to love when nobody would eat those and leave them all behind for me!
i’m a ricard fan myself 
What I find interesting is the different sweetness levels involved. From the dry bitter Absinthes to the near diabetes inducing sweetness of Sambuca and some Araks, it is all over the map
Don’t forget Anisette. And some people would include Strega in the list as well.
Sorry. The gimmick I was going for was that there would be one from each country, and absinthe looked more famous. Also, the only aguardiente I have tried was anise flavored. Mixed very well with Coke and lime.
Assuming we’re talking about shots (and I don’t think I’d sip any of them), I prefer the non-syrupy types. A crisp, clean ouzo would probably be my choice.
ETA: Or aquardiente!
Yeah, there is a mixing of categories of drinks going on. I’d certainly put Jager in a different category (herbal bitters/herbal liqueurs–along with others like Chartreuse, Unicum, Underberg, Galliano, etc., all of which have an anise component, but a bit more than just that going on.) Even absinthe should probably be in a different category, as its defining characteristic is wormwood as much as it is anise, but it’s close enough that I’d count it.
Disqualifying Jager, I’d go with French pastis–Pernod or Ricard’s are fine and commonly available. They are a wonderfully refreshing summer drink, mixed about 5 parts pastis to 1 part water over ice.
I thought you were going to say Fernet Branca. I hate Fernet. I’ve tried the first four on your list, and am tempted to try the rest in an effort to broaden my booze horizons, but I shant fake the funk. I can happily live without anise flavored everything.
Another one is Herbsaint from New Orleans
I love anise and have drank all of the above over the years, but have mostly settled on absinthe. For what it’s worth, it first came from Switzerland and not from France. I take mine in a nice Pontarlier glass through a dripper. I don’t think that decent absinthe needs sugar, but that’s just my taste.
You were right the first time on the Pacifique. That’s one of my favorite bottles bar none, and it is relatively easy to get.