My work has mainly been on geometric algorithms, and in particular on algorithms that have provable properties, but are relatively simple. Randomization is quite useful for this, whether via the Vapnik-Chervonenkis dimension, or using the general framework introduced here. See, for example, a survey on randomized geometric algorithms.
I've coded up a data structure for nearest neighbor searching in metric spaces, which supports nearest neighbor queries, fixed radius queries, and k'th-nearest-neighbor queries. I've tested it on Euclidean data, strings under Hamming and edit distances, and some bitvector datasets. It gives a pretty good speedup for low-dimensional data, and sometimes high-dimensional data, but isn't going to be as fast as more specialized methods.
I am co-moderator of the compgeom-announce mailing list, for announcements regarding computational geometry, and the list compgeom-discuss, for discussions.Sadly, I haven't managed to:
Introducing the Collectibles! Meet the Collectibles!
And finally, sometimes we must bite the bull by the horns.