This depends on how you define "democracy" - specifically whether restrictions on the franchise, such as those against women, those who did not own property, or those against racial minorities, are considered as dis-qualifiers. If no, in this case, San Marino would be a good candidate, with their legislature dating back to the 13th century. Furthermore, some governments have democratic institutions, but were not necessarily completely sovereign at various points - the Isle of Man and Iceland both come to mind here.

If you mean oldest democracy in which everyone can actually vote, then it would be Finland, which outlawed restrictions based on sex or ethnicity in 1906.