The number of possible word forms is theoretically infinite in agglutinative languages. This brings up the out-of-vocabulary (OOV) issue for part-of-speech (PoS) tagging in agglutinative languages. Since inflectional morphology does not change the PoS tag of a word, we propose to learn stems along with PoS tags simultaneously. Therefore, we aim to overcome the sparsity problem by reducing word forms into their stems. We adopt a Bayesian model that is fully unsupervised. We build a Hidden Markov Model for PoS tagging where the stems are emitted through hidden states. Several versions of the model are introduced in order to observe the effects of different dependencies throughout the corpus, such as the dependency between stems and PoS tags or between PoS tags and affixes. Additionally, we use neural word embeddings to estimate the semantic similarity between the word form and stem. We use the semantic similarity as prior information to discover the actual stem of a word since inflection does not change the meaning of a word. We compare our models with other unsupervised stemming and PoS tagging models on Turkish, Hungarian, Finnish, Basque, and English. The results show that a joint model for PoS tagging and stemming improves on an independent PoS tagger and stemmer in agglutinative languages.