Scikit-Learn: The most comprehensive Machine Learning package in Python:
http://scikit-learn.org/stable/

Tensorflow: A well-known solution for Deep Learning from Google:
https://www.tensorflow.org

MLPACK: Machine Learning using C++ and Unix Command Line:
http://www.mlpack.org

Word2Vec: One of the well-known packages for Natural Language Processing:
https://deeplearning4j.org/word2vec

Vowpal Wabbit: Excellent Machine Learning software used in many Kaggle competitions:
https://github.com/JohnLangford/vowpal_wabbit/wiki/Tutorial

LIBSVM & LIBLINEAR: Highly regarded command line machine learning tools:
https://www.csie.ntu.edu.tw/~cjlin/libsvm/
https://www.csie.ntu.edu.tw/~cjlin/liblinear/

LIBFM: Matrix Factorization:
http://www.libfm.org

PaddlePaddle: Deep Learning from Baidu:
https://github.com/PaddlePaddle/Paddle

CuDNN: Deep Learning/Neural Network solution from NVIDIA:
https://developer.nvidia.com/cudnn

Caffe: Deep Learning framework from Berkeley:
http://caffe.berkeleyvision.org

Theano: GPU Enabled Machine Learning in Python:
http://deeplearning.net/software/theano/

Torch: High performance Machine Learning in Lua:
http://torch.ch

Keras: Open-Source Neural Network Applications:
https://keras.io