For my problem (1000+ total classes, 1 class per input), I experimented with Naive Bayes + TFIDF (~50% accuracy, < 1 sec training), then Word2vec + CNN model on GPU (~70% accuracy, 6 hrs training), and finally FastText (99% accuracy, 10 minutes training).
FastText [0] in particular is quite impressive. It is essentially a variant of Word2Vec that also supports n-grams, and there is a default implementation in C++ with a built-in classifier that runs on the command-line (no need to setup Tensorflow or anything like that).
Despite it only running on plain CPUs and only supporting a linear classifier, it seems to beat GPU-trained Word2Vec CNN models in both accuracy and speed in my use cases. I later discovered this paper from the authors comparing CNNs (and other algorithms) to FastText, and their results track my experiences [1].
This goes to show that while GPU-accelerated models are cool, sometimes using a simpler, more suitable model can have a significantly better pay-off.