There are around 100 classification and regression models which are trainable via the caret packagecaret package. Any of the classification models will be an option for you (as opposed to regression models, which require a continuous response). For example to train a random forest:
library(caret) train(response~., data, method="rf")
See the caret model training vignette which comes with the distribution for a full list of the models available. It is split into dual-use and classification models (both of which you can use) and regression-only (which you can't). caret will automatically train the parameters for your chosen model for you.