Is there a good shuttle service? Taxis? What should one expect to pay? Is it worth pre-arranging?
While Ivan's answer is the most economical option, I disagree that there's not a shuttle. For inexperienced travellers who may not speak the language, there ARE taxis from both airports as well.
There is also a shuttle/bus company called Manuel Tienda León. I used them. For 45-50 ARS, they'll take you to the city to just near Retiro (the main bus station and a metro station), and for 5 ARS extra, you can get dropped at your hostel/hotel.
To me this was the best deal after a crazy long flight from Europe with delays, versus having to negotiate with local buses and being unwilling to pay for taxis.
Even now, with my improved Spanish skills, I'd probably still go for the shuttle option if arriving on my own by plane. No need to pre-arrange though, they're right as you enter the terminal, and you don't have to wait more than 15 minutes for a shuttle.
If you are arriving from an international flight, you will probably land in Ezeiza (EZE). There you have two good options:
I personally do not advise you to take the bus as it can be a long and uncomfortable trip.
In Buenos Aires there are 2 airports: Aeroparque (AEP) and Ezeiza (EZE). First one is smaller and closer to the city center.
If you arrive to AEP you have to take a "colectivo". It's a bus that goes from the airport to the center stopping when somebody pushes the stop button. Very easy :) When I was in Buenos Aires (2008), it cost 1$ (ARS, about 0'20 dolars). Also you can take a taxi for 20$ (ARS) if you arrive late or too early.
If you arrive to EZE you have to take bus number 86 that arrives to Plaza de Mayo in the city center. I don't remember the price, but it was.. cheap ;) A taxi from EZE may be really expensive due it's far from city center.
So, you don't need to pre-arrange, there is not any special "shuttle" that worth to pay for it and use taxi only if you arrive to AEP. I hope it helps!