practical successes of semi-supervised learning?

In my (admitedly small) experience with generative models (mainly in NLP) using unlabeled data usually helps (unless there is far more unlabeled than labeled data), but I haven't done anything worth calling a success.

In many cases in NLP you can get by with very little (or no) labeled data and still get good results. Some examples are transfer learning of dependency parsing (Ganchev et al, Dependency Grammar Induction via Bitext Projection Constraints) where you can use a parser for one language to induce one in another using only aligned text (and finding aligned text is cheaper than actually building a treebank) or prototype learning for sequence models (Haghighi and Klein, Prototype-driven learning for sequence modeling), where you can just give a few prototypes (which do not constitute labeled data) and get surprisingly good POS tagging and information extraction. Both of these works only use labeled data to evaluate the algorithms, which are close to unsupervised in their inner working. There are lots of examples of unlabeled data helping some results slightly, but I think you're asking for radical changes.

Co-training is a semi-supervised learning algorithm that is simple yet has had a great deal of success, evident by the fact that the influential Blum & Mitchell paper Combining Labeled and Unlabeled Data with Co-Training from COLT 1998 got the ICML 2008 10 years best paper award. There have been a lot of variants of co-training that people use.

BTW, you mentioned about active learning. Note that there are various ways you can combine active learning with semi-supervised learning. See this paper "Combining Active Learning and Semi-Supervised Learning Using Gaussian Fields and Harmonic Functions" which discusses one such approach.

Or, what if you ignored the labels, and just used an unsupervised approach?

I've been wondering a similar question about transduction. Transduction uses unlabelled data at training time by only computing predictions on those points instead of inferring a general learning rule. There are some formulations which use kernels and graphs and are closely related to spectral clustering. My advisor told me that in practice the presence of labels doesn't actually help, you could do just as well ignoring them and simply spectral clustering the data. My question is, has transduction been used for any practical problem?

I've been working on semi-supervised learning for identity inference, using an approach similar to what's been outlined in this paper. So identity inference/face recognition is a huge area. An interesting consequence of this research is that far simpler feature functions can be used than (to my understanding) what has been used in the Vision community to track similarity.

Closely related to some of the methods you mentioned (transductive label propagation, with some corrections for small amounts of labeled positive examples) is the algorithm that powers the GeneMANIA gene function prediction server. Basically it acts as a recommendation engine for genes powered by graphs derived from high-throughput biological assays, and a browser interface on top of those graphs (full disclosure: I was heavily involved in the development). Because the graphs are aggressively sparsified, you can run the inference procedure on a customized composite graph at the speeds necessary for a live response over the web, despite outperforming algorithms that require far more computational overhead on a recent benchmark of gene function prediction in mouse. That's pretty practical, don't you think?

See Mostafavi et al, 2008 for algorithmic details and, to a lesser extent, Warde-Farley et al, 2010 for the more application-related details.