This depends on the carburetter type. We'll go through the popular models...
H/HV Type (Cork Seals): The most common reason for leakage on this type of carburetter is related to the cork seals surrounding the jet. If they are poorly seated or quite old and dry then obviously the fuel will be able to leak, either around or through the cork material. In this instance the best cure is to replace all seals taking great care to fit correctly. When the seals are leaking on a new carburetter, one that has been standing for some time or just after fitting new seals this is normally because they have not been soaked in oil. In this instance remove the seals carefully and place in a bath of oil over night. Upon refitting the leaking should be cured.
HS Type (Plastic Jet Tube): With this type of carburetter leakage is normally found in the area of the connection between jet tube and float bowl. The most common reason for this is the ill fitment or degredation of the small rubber seal on the end of the jet tube. Replacement of this seal whilst taking great care to seat correctly should cure the problem but don't rule out other possibilities such as a stripped thread on the connecting bolt, a kinked or split jet tube or worn seating on the float bowl.
HD Type (Diaphragm Jet): Most commonly, leakage from this type of jet is related to the diaphragm connected to the base of the jet. If this diaphragm becomes brittle over time, worn by use or is incorrectly fitted then leakage could occur. To check, remove the jet completely and if any wear or damage is discovered, replace the jet and diaphragm assembly taking care to seat the diaphragm correctly.