This is a common problem. Most TVs with USB ports only show pictures. (I know...how lame!) and most of the TVs that do support video formats only support a few file formats.
No, a USB-to-HDMI adapter need a PC's brains to make it work. It will not work between a hard disk and a TV. (If that's what You meant.)
Like BmwManiac said, You could use a laptop with an HDMI out. A USB-to-HDMI adapter might work with a laptop. (If that's what You meant.)
***I use a High Definition Media Player (HDMP.) Search eBay for "HD Media Player." A HDMP will let You plug in a USB hard disk, and will play videos on a TV via a HDMI port. It will come with a remote. Prices start under $30, and go up to $600. A cheap one will do what You need.