Slovakia will become the 16th of the current 27 members of the European Union to adopt the Euro as its currency on 1 January 2009. The fixed conversion rate between the Euro (EUR) and the existing Slovak national currency (SKK) is €1 = 30.1260 SKK.
The 15 EU countries currently using the Euro as their currency are: Austria, Belgium, Cyprus, Finland, France, Germany, Greece, Ireland, Italy, Luxembourg, Malta, the Netherlands, Portugal, Slovenia and Spain.
Of the other 11 countries, two (Denmark and the UK) have negotiated opt-outs which mean they have no obligation, ever, to adopt the Euro as their currency if they do not wish to do so. The main Swedish political parties have agreed not to join the Euro until approval in a national referendum is given; a referendum in 2003 rejected adoption so Sweden has chosen not to join ERM II. Full details of each EU member's status vis-a-vis the Euro may be viewed here.
You can see images of the Euro coins being issued by Slovakia to coincide with its adoption of the Euro as its currency here. Euro notes are uniform throughout the Eurozone and show no differences from country to country.