An electric blender is useful, especially for drinks like frozen daiquiris and those with ingredients that are not easily combined, but it is not essential To puree fruit, whip cream, or prepare frozen drinks, frappes and milk shakes, you need a blender with continuous speed adjustment or you can use an everyday food processor. If drinks with crushed ice become a regular request at your bar or you host many cocktail parties, consider investing in an electric ice shaver.
Use a standard ice bucket, widely available in various sizes and materials, to keep frozen ice cubes conveniently at hand for the duration of any party or cocktail session. Ice tongs or an ice shovel are ideal to remove the ice from the bucket (do not use your fingers), but if you do not have either, use a large spoon.
Fresh fruit juices can be prepared using a lemon squeezer or juicer. (Electric juicers are not recommended because they squash the peel and seeds, too.) Many long drinks contain soda water, which is best added to the glass using a siphon. To use one, you simply fill the siphon with water from the faucet or use still mineral water. A carbon dioxide cartridge will make sure the water is always carbonated when you want it.
Another very useful tool is a pair of bar tongs, which can be used to loosen tight corks in champagne and other sparkling wines. A bitters or dash bottle has a doser cap and is good for storing ingredients that are only used in small dashes.
The other pieces of equipment that help to make your job behind the bar enjoyable are standard in most kitchens. These include a lemon squeezer and a nutmeg grater. No doubt your kitchen also contains a chopping board (preferably with a drainage channel), a finely serrated knife, similar to a cheese knife, with two points for spearing pieces of fruit, and a citrus zester, also called a cannelle knife, for removing fine strips of citrus peel that make attractive garnishes.
Small dishes for holding pieces of fruit and garnishes are also useful, as is a cork with a pouring spout, which can be inserted into any bottle to make pouring out measures easier. Of course you also need a can opener, a bottle opener, and a (orkscrew. A champagne or bottle cooler is indispensable. Toothpicks are an absolute must for spearing olives, cherries, and pearl onions, as well as for creating other garnishes.
You might also want to stock up on brightly colored drinking straws in varying lengths if you plan to serve some of the more exotic cocktails. (Be sure to avoid straws which are too thin, otherwise pieces of ice or fruit can block them.)