Yes! HDMI is basically a DVI with audio already integrated. A DVI is a pure video (thus the Digital Video Input/Interface) while a HDMI (High Definition Multimedia Input/Interface) combines both the video and audio and digitally inputted to the display or monitor/TV. In fact, this will probably the future standard interface since it only requires one plug connection to do both the video and audio.
If the interface from your multimedia source (DVD/Projector/TV) only comes in DVI then you will need a DVI->HMDI adapter.