Soomething like this might give you results you're looking for (you can select whichever property of the media file you need):

List<string> FindAllFiles(ContentFolder contentFolder, IContentRepository repo, List<string> seed)
{
    seed.AddRange(repo.GetChildren<MediaData>(contentFolder.ContentLink).Select(f => f.Name));

    foreach (var f in repo.GetChildren<ContentFolder>(contentFolder.ContentLink))
    {
        FindAllFiles(f, repo, seed);
    }

    return seed;
}

var folder = _repository.Get<ContentFolder>(SiteDefinition.Current.GlobalAssetsRoot);
var allFiles = FindAllFiles(folder, _repository, new List<string>());

`_repository` is just a injected implemention of IContentRepository. Usually you can ask these dependencies via constructor of the class.

A bit different approach from valdis:

var descendents = _contentRepository.GetDescendents(SiteDefinition.Current.GlobalAssetRoot);

foreach (var descendent in descendents)

{

 var path = _fileBlobProvider.Get(contentLink).BinaryData as FileBlob).FilePath;

//do as you wish with the path

 }

note that if you have a lot of assets, it might be a good idea to use GetChildren with paging instead.