Depends on which searches are being done.
Usually it's a Local Search (as described by buildersmate above) and Drainage & Water maybe Coal, Environment, Chancel Repair Liability or Commons.
There are all kinds of other searches depending on the area from special mining searches in parts of Cheshire and Cornwall to highways, utilities, London Underground, all sorts of things.
There are also Land Registry searches, these are different in registered (OS1 priority search and K17 bankruptcy) and unregistered land (Land Charges).
There are also more specific searches depending on the property and area like manorial rights.
Is it a particular search or issue you are enquiring about for more details?