Statistical query model algorithms?
Almost every algorithm that works in the PAC model (with the exception of parity learning algorithms) can be made to work in the SQ model. See e.g. this paper of Blum et al. in which several popular algorithms are translated into their SQ equivalents (Practical Privacy: the SuLQ framework). The paper is in principle concerned with "privacy", but you can ignore that -- it is really just implementing algorithms with SQ queries. 

Agnostic learning, on the other hand, is much harder in the SQ model: computational issues aside (though these are important), the sample complexity required for agnostic learning is roughly the same as that required for exact learning, if you actually have access to the data points. On the other hand, agnostic learning becomes much harder in the SQ model -- you will usually need to make superpolynomially many queries, even for classes as simple as monotone disjunctions. See this paper by Feldman (A complete characterization of statistical query learning with applications to evolvability) or this recent paper by Gupta et al. (Privately Releasing Conjunctions and the Statistical Query Barrier)