If you are disciplined, and separate data into training and testing sets, you can try as many models as you want without fear of overfitting. Indeed, optimizing over the parameters of a model on the training set is essential (pruning parameters in a tree, regularization weights, etc.) and can be thought of as training large number of models.

If you aren't doing this correctly, then you can't really interpret the performance of even a single model. Seen people screw this up in so many ways - my favorite recent one that was quite high on HN was someone using the full dataset for variable selection, before doing a training-testing split afterwards.