The Loebner (on the NLP side) this year should be interesting - http://www.aisb.org.uk/events/loebner-prize - on the AI planning side usually the StarCraft competitions - https://sscaitournament.com - interested to see how DeepMind performs.

On NLP side, many subfields tend to run annual shared task competitions, e.g. SemEval (http://alt.qcri.org/semeval2017/index.php?id=tasks) or TAC (https://tac.nist.gov/) for semantic analysis, WMT (http://www.statmt.org/wmt17/index.html) for machine translation, etc etc.

(Disclaimer: I work at Nexar)

Nexar just released Nexet, a large dataset of 55K road images (5K of which are labeled). I think it's an interesting one as the images were captured by mobile phones (setup as dashcams), so you get "real world" data. Of-course there's an accompanying competition coming up: https://www.getnexar.com/challenge-2/

Kaggle, The Netflix Challenge, CASP

The non-profit platform https://www.crowdAI.org currently hosts a NIPS 2017 challenge as well as a genetic challenge, and constantly adds new challenges. Btw, it's completely open source, and keen on having contributors to help build the open challenge platform the community wants the most.

There's WIDERFace(http://mmlab.ie.cuhk.edu.hk/projects/WIDERFace/index.html) which is specific to facial recognition.

MS COCO, although i think that's part of the imagenet contest now.

slightly different, but wanted to add numer.ai to the great list others have commented