The entire medieval period (roughly dating from the beginning of the so-called 'Dark Ages' right through to the English Reformation). I find it absolutely fascinating, for various objective and subjective reasons. Have read loads about it, for fun and general interest as well as for my courses at university. For my two dissertations this year, I'm doing one on the will of Elizabeth Montagu, countess of Salisbury (who died in 1415), and the other on the connections and relationships between pre-Reformation Christmas carols and contemporary social customs/ceremonies.
To be honest I find it hard to see how anyone could possibly prefer modern history. Having done my entire two years of GCSE solely on 20th century history, it was such a breath of fresh air to look at the Wars of the Roses at AS, you'd find it hard to believe!
I don't know why, but even something I would find dull today, or anywhen in the modern period I suppose (such as economics), is more interesting to me when you look back a few hundred years. Generally, the older something is, the more interesting it is...though obviously you have to draw a line somewhere. Not that I don't like ancient history though, because I do!