The Czech Republic seems to be fond of very strong alcohol. Besides their 70% by volume Absinthe, they also have a great many varieties of fruit-based brandy. The main one of these is Slivovice.

It's made from Plums though there is only a slight aftertaste of such evident amongst the brands I have tried. The quality is variable but it is a white spirit and the alcohol content is 50% by volume (100 proof for the USians). The extremely high alcohol content is one possible explanation of why there is no aftertaste evident, your tastebuds have given up and retired for the evening by the time the aftertaste would be rolling around. This is not a spirit for subtle drinking but rather for taking harsh shots of or using to give something nicer a desired kick. I've yet to try mixing it but I suspect lemonade would be a good choice. It would probably also be good for slings especially those made with fruit juice.

Other varieties seen include Brandy made from Cherry (Trešnovice), Strawberry (Jahodvice) and Apricot (Meruňkovice). Brewing these varieties is said to be a Czech past-time with many rural families having their own private recipes (the homebrew varient is called Domaci), some of which have gone on to become established brands.

A rough recipe is as follows:

Take a large jar of plums and squeeze but not squash each slightly until the skin is broken and their juice flows slightly but they are largely intact.
Place in a jar and seal for several months, a recipe I read suggests burying the jar.
Remove the mixture from the jar, discarding the fruit pulp which should have sunk to the bottom.
Distill twice and dilute with water down to the desired strength (stop while it's still flammable).

At time of noding, this is a very cheap drink with a sample-sized bottle (about 5cl) costing little more than a beer at 60Kr (currently ~1.5GBP). A hip flask with .2 litres cost me 300Kr (~7GBP) Duty-Free.

It is not for the faint hearted but if you dare then the Czech for cheers/salute is Nazdravi and one Czech toast is to clink the top of the glasses, then the bottom then touch it to the table before downing the shot.

Update: It exists elsewhere as Slivovitz, I didn't think to search for linguistic varients. I have personally heard of a drink by this name from Yugoslavia. Damodred tells me that the Polish know it as Sliwowica and that the homemade version thrived when homebrewed alcohol was forbidden.

Further Update: It goes well with Coconut and Pineapple juice.

Yet Another Update: A rather cute Czech bartender I met in Edinburgh assures me that the alternatives such as Jahodvice (but not Trešnovice) are almost certainly just for the tourists. She also elaborates on the traditional toast by adding that eye-contact should be maintained throughout the ritual and to break it demonstrates insincerity but she may have just been flirting.

Lonely Planet: Czech and Slovak Republics
Czech expats.
Tastebud numbing personal experience.