How old is Arthur Conan Doyle's character Sherlock Holmes?

There are two ways your question might be interpreted, and I will answer both forms. 

The Sherlock Holmes stories are over a century old. The first time Sherlock Holmes made an appearance in print was in 1887 with the story A Study in Scarlet. Sir Arthur Conan Doyle published a total of fifty-six short stories and four novels, with the final installments having been published in 1927. The stories themselves are presumed to take place between 1880 and 1914, based on textual evidence. 

Such personal details like Mr. Holmes age and date of birth are actually a bit of a mystery themselves! Our best guess comes from His Last Bow, where Holmes is described as having been sixty years old. As the story was published in 1914, we can guess that Holmes was born in 1854. That means that if the earliest stories date from at least 1880, Holmes was between the ages of 26 and 60 throughout the entire run of publication.