Where can I find free spatio-temporal dataset for download?

You can get yellow and green taxi trip records from NYC taxi dataset. The website collects data from 2009 until now. You can download the data from the following link: http://www.nyc.gov/html/tlc/html/about/trip_record_data.shtml

If you have R and the spacetime package then you are only data(package="spacetime") away from a list of space-time data sets bundled with the package:

Data sets in package ‘spacetime’:

DE_NUTS1 (air)          Air quality data, rural background PM10 in
                        Germany, daily averages 1998-2009
fires                   Northern Los Angeles County Fires
rural (air)             Air quality data, rural background PM10 in
                        Germany, daily averages 1998-2009

then for example:

> data(fires)
> str(fires)
'data.frame':   313 obs. of  3 variables:
 $ Time: int  5863 5870 6017 6018 6034 6060 6176 6364 6366 6372 ...
 $ X   : num  63.9 64.3 64.1 64 64.4 ...
 $ Y   : num  19.4 20.1 19.7 19.8 20.3 ...

Another idea is to combine OpenStreetMap project map data, for example, using corresponding nice R package (http://www.r-bloggers.com/the-openstreetmap-package-opens-up), with census data (population census data, such as the US data: http://www.census.gov/data/data-tools.html, as well as census data in other categories: http://national.census.okfn.org) to analyze temporal patterns of geosocial trends. HTH.

First thing that came to mind would be one's personal workout data from running or biking apps.

Otherwise there is a dataset around NYC's taxi trip data. Quick Googling brought me this: http://www.andresmh.com/nyctaxitrips/. Variables include time and location for both pickups and dropoffs.

Another dataset comes from Chicago's bikesharing service. It can be found here: https://www.divvybikes.com/datachallenge.

You can get some documented, publicly available EEG data from the HeadIT database at UCSD. http://headit-beta.ucsd.edu/studies

The data itself appears to be in Biosemi Data Format (.bdf) files, described here: http://www.biosemi.com/faq/file_format.htm

Biosemi provides links to several open-source methods to access and import .bdf files on their website, including several functions for importing into Matlab, as well as into Python (BioSig) and C/C++ libraries: http://www.biosemi.com/download.htm

Just as a forewarning, EEG data can be a bit of a bear to work with, due to it's inherently low signal/noise ratio.