We live in a ~100 year old house and absolutely love it.
One benefit about older homes is (typically) location. We are located in the old part of town and are very close to the grocery store (2 blocks) restaurants, stores, bars, wife's work, library, parks, etc, etc.
Also, our home underwent an interior renovation by the previous owner (they bought it from a dead beat alcoholic, renovated the inside and flipped it) It was well worth it for us, as we had completely redone our previous house (1920s construction) and didn't have the energy to do another one. The exteriour was in shambles, though, so we spent our for 2 summers sprucing up the outside of the house and landscaping the yard - which we both enjoyed immensly).
Downside of old homes: expensive items *will* eventually come up. We had to replace our roof last year, and while we were getting that rolling, realized that we should probably have the chimney rebricked while we were at it. But, we couldn't just get a new roof, we needed to somehow improve the house, so we went ahead and had 2 skylights and a 'solar tube' installed to brighten up the upstairs. We're very glad we did it, though - looks great w/ the newer 'dimensional' shingles.
I can certainly see the attraction to new construction, but location was our biggest criteria in purchasing a few years back, and old construction was pretty much the only option in the area we want to live.