Simple answer -- on newer equipment yes (although other connection mechanisms are usually also present for non-HD or legacy equipment connection).
HDMI (and HDCP compliant devices) is the way to go on new equipment but it takes a bit of explanation as to why.
First HDMI is a connection mechanism which passes both digital multichannel audio and video at any resolution up to and including 1080p. For reasons explained below it can be used for non-HD material (e.g. CD audio, DVD video and audio) but in the immediate future will be a must for HD.
First ... the issue. Owners of copyrighted HD digital material are concerned about piracy. Therefore they have promoted adoption of an encryption scheme to prevent connection of unauthorized devices which would allow copying of HD digital signals.
This is known as HDCP (High-bandwidth digital copy protection). While not fully in place yet, because so many people still have older Tvs and equipment that doesn't support HDMI, it is expected to be in place in the next 2-3 years. It is complex to explain, but basically unless a connection is made between HDCP compliant devices the signal is cut off or down-sampled to non-HD quality. This means that consumers will not be able to enjoy HD programming (on TV or disk) unless they have HDCP compliant devices at all points that originate, switch, process or display HD programming.
Devices impacted by this include DVD players that output HD resolution (upconverting DVD players), HD DVD and Blu-bay disk players, HDTVs and home thatre receivers that switch or process HD signals.
The common connection mechanism is an HDMI cable.
If two HDCP compliant devices are connected via HDMI they will allow the HD program to be processed. If either device is not HDCP compliant the signal will be cut off (or if connected via an analog cable (e.g. component video) will be reduced to non-HD resolution. This will --- at least in theory -- work transparently to the user (and increasingly this is the case as early bugs are being worked through).
So, if you plan on a HDTV (or HD projector) make sure it is HDCP compliant, and has HDMI inputs. If you plan to switch HD sources (e.g. an HD cable or satellite box/PVR, Upconverting DVD player, Blu-ray or HD DVD player) going into a TV (or projector) you need more than one connector, or to use an A/V receiver with HDMI switching capability to do the selection. The advantage of the A/V receiver is that it allows the video to be sent to the HDTV (or projector) and the audio to be processed in the receiver and sent to the connected surround sound speakers.
All the newer equipment being sold is available with HDMI connections and HDCP compliant. It's just necessary to make sure this is part of the requirements you specify when choosing.
I hope this answered your question.