For high spatial resolution, you can download Sentinel-2 data. It has worldwide cover every ten (very soon 5) days. You have 10 meter bands in Red and NIR, so you can compute ten meter NDVI (vs 30 m with Landsat). Make sure that you use the L2A images (radiometrically corrected with SEN2COR) in order to compute a meaningfull NDVI value from the "Top of Canopy" reflectance (NIR-Red)/(NIR+Red).

Primary download site for Sentinel

https://scihub.copernicus.eu/dhus/#/home

alternative solutions can be found on https://gis.stackexchange.com/questions/190681/where-how-to-download-sentinel-2-images


If you are more interested in the temporal resolution than in the spatial resolution, daily images are available from Sentinel-3 (soon), PROBA-V or MODIS. Again, I recommend using TOA (level2) images.

PROBA-V : http://aida.vgt.vito.be/content/products

MODIS (and also Landsat): https://earthexplorer.usgs.gov/