Here we present experimental realizations of two new entanglement detection methods: a three-measurement Bell inequality inequivalent to the Clauser-Horne-Shimony-Holt inequality and a nonlinear Bell-type inequality based on the negativity measure. In addition, we provide an experimental and theoretical comparison between these new methods and several techniques already in use: the traditional Clauser-Horne-Shimony-Holt inequality, the entanglement witness, and complete state tomography.