List of NLP challenges
List of NLP competitions on Kaggle by popularity [number of teams]:


Two Sigma Connect: Rental Listing Inquiries [2709 teams]
https://www.kaggle.com/c/two-sigma-connect-rental-listing-inquiries   
Home Depot Product Search Relevance [2125 teams]
https://www.kaggle.com/c/home-depot-product-search-relevance   
Quora Question Pairs [2123 teams]
https://www.kaggle.com/c/quora-question-pairs   
What's Cooking? [1388 teams] https://www.kaggle.com/c/whats-cooking   
Crowdflower Search Results Relevance [1326 teams]
https://www.kaggle.com/c/crowdflower-search-relevance   
Bag of Words Meets Bags of Popcorn [578 teams]
https://www.kaggle.com/c/word2vec-nlp-tutorial   
Transfer Learning on Stack Exchange Tags [380 teams]
https://www.kaggle.com/c/transfer-learning-on-stack-exchange-tags/data   
Facebook Recruiting III - Keyword Extraction [367 teams] https://www.kaggle.com/c/facebook-recruiting-iii-keyword-extraction


New entrants are prohibited, you won't be able to download data for this competition   

Dato: Truly Native? [274 teams] https://www.kaggle.com/c/dato-native   
The Allen AI Science Challenge [170 teams]
https://www.kaggle.com/c/the-allen-ai-science-challenge