Nuclear magnetic resonance (NMR) spectroscopy is an innovative method for wine analysis. Every grapevine variety has a unique structural formula, which can be considered as the genetic fingerprint of the plant. This specificity appears in the composition of the final product (wine). In the present study, the originality of Hungarian wines was investigated with 1H NMR-spectroscopy considering 861 wine samples of four varieties (Cabernet Sauvignon, Blaufränkisch, Merlot, and Pinot Noir) that were collected from two wine regions (Villány, Eger) in 2015 and 2016. The aim of our analysis was to classify these varieties and region and to select the most important traits from the observed 22 ones (alcohols, sugars, acids, decomposition products, biogene amines, polyphenols, fermentation compounds, etc.) in order to detect their effect in the identification. From the tested four classification methods—linear discriminant analysis (LDA), neural networks (NN), support vector machines (SVM), and random forest (RF)—the last two were the most successful according to their accuracy. Based on 1000 runs for each, we report the classification results and show that NMR analysis completed with machine learning methods such as SVM or RF might be a successfully applicable approach for wine identification.