I think the best thing about researching my family history has been all the near and far flung family I have got to know either in person or online. However, one of the most unusual connections I've made recently happened whilst I was visiting Dublin with my partner earlier this year. Although I was under strict instructions not to spend all of his birthday weekend "dead-diving" as he sarcastically terms my serious research, we did manage to visit the beautiful National Library of Ireland. Whilst there, it would have been criminal not to have had a quick peek at something genealogical, so we ordered some Carlow newspapers on microfilm. The lady standing next to us heard us talking and it turned out she was researching EXACTLY the same man! We have compared notes since and have discovered we are indeed distantly related (and via marriage on her side to Walt Disney of all people!)
So, you see, fate must have intervened that day and perhaps it will inspire you to get chatting to some of your fellow researchers at the next archive or library you visit. Actually, there's an idea - being able to add your details to a Surname board in the foyer for others to see and leave you their own in return perhaps?