In almost all cases, cell lines are available. For most samples, cell lines are held at the Coriell Cell Repository. Samples from HGDP are available at CEPH.
Coriell hold detailed information on the 1000 Genomes Project populations and sample collection process.
Individual sample pages in the data portal include links to the repository where the cell line is available.
The main exception to the above is around 400 samples in the Gambian Genome Variation Project (GGVP), for which cell lines are not available.