Open PFLOW project offers:
open dataset for typical people mass movement in urban areas
Tokyo metropolitan area is available and Chukyo metropolitan area seems to be under preparation.
Details can be found in a recent publication:
Takehiro Kashiyama, Yanbo Pang, Yoshihide Sekimoto, Open PFLOW:
Creation and evaluation of an open dataset for typical people mass
movement in urban areas, Transportation Research Part C: Emerging
Technologies (2017) Volume 85, Pages 249–267.
T-Drive trajectory dataset is a recent find. It provides:
a one-week trajectories of 10,357 taxis. The total number of points in
this dataset is about 15 million and the total distance of the
trajectories reaches 9 million kilometres.
Although not about human movements, Liquid Robotics company makes available interesting dataset from its PacX challenge. Data about location and environmental sensor readings of four robot gliders sailing through Pacific Ocean are available for download. More info about (really cool) project on the blog, via WIRED and this talk.
Another option to tackle the privacy issues would be to use animal tracking data. I guess data protection will be less of an issue here. As an advantage, you might still be able to test your software/methods with real world movement data. Disadvantage might be that if your application needs 'human specific' movements - they might not fit your purpose.
Have a look at Movebank or DRYAD websites to check if some of their data might fit into your project.
Yet another option is the spatial part of the Chris Whong's NYC taxi data. They only provide pick up and drop off locations, however the volume (11 GB!) and contextual info (fare, passengers, etc.) make them really attractive (alternative download, more info about privacy concerns raised by the data).
Urška Demšar's post on her recent paper on 'Analysis of Human Mobility from Volunteered Movement Data and Contextual Information' promises:
There will also be a free data set of volunteered GPS trajectories
linked to this paper available soon. Stay tuned.
Update: paper mentions that data will be available on CRAWDAD mentioned by @ejel but I havent found it there.
Another option might be to create synthetic dataset yourself. If you need some inspiration look at recent paper by van Dijk J (2018)
Identifying activity-travel points from GPS-data with multiple moving windows
Computers, Environment and Urban Systems (link). More details are provided in paper's appendix and code and example dataset are available on github.