Start here: http://en.wikipedia.org/wiki/Statistical_classification#Algorithms

Which is "best" depends on what you want to do.

You might also want to consider the amount of labeled and unlabeled data available to you. Some algorithms can work with very few seeds (e.g. label propagation).

Co-training is one of the most widely used techniques for semi-supervised classification. It is flexible because you can use popular classifiers like SVM, random forest as base classifiers with co-training. Here is a paper for the reference:

http://www.u.arizona.edu/~echan3/539/BlumMitchell98.pdf

The other method you could use if a Graph based semi-supervised method, which is easy to understand and use. Other methods include Transductive SVM and random walks.