'Hochdeutsch' (lit. "High German") in the meaning 'Standarddeutsch' can be considered the German variant of received pronunciation. It is spoken nowhere naturally, currently the people living around Hannover are considered to come closest to this language with their dialect.
'Hochdeutsch' should not be confused with 'Hochdeutsche Dialekte' which are both translated as 'High German'. Only the first is synonymous with 'Standarddeutsch', the latter is the group of dialects spoken on higher grounds (the more southern regions).
What is and what's not Hochdeutsch?
Since there is no common instance of language control like in other countries the 'Hochdeutsch' is a different one for each country where German is spoken and can be seen as a composition to balance the language. According to en.wikipedia.org it originates with the written language. The most important milestones should be the Lutherian Bible and Grimm's Fairy Tales.
German as a language originated with the people living in the Sacrum Romanum Imperium (Heiliges Römisches Reich Deutscher Nation) where the royalties spoke Latin or French. With time the people's language gathered more and more power, first shown in having church services in German and then forming the German Empire where the language defined the people opposed to other countries where the process was in the other direction. This process took very long. High German was considered a purely written language at least until 1800.
How does Hochdeutsch sound?
As mentioned above, there is no the-one-and-only Hochdeutsch. In Germany it's called 'Hochdeutsch', in Austria 'höheres Deutsch' and I bet the Swiss have their own word for it.
The general rule is to speak every syllable as clearly as possible. Additionally, you don't use contractions ('Tut es weh?' rather than 'Tut's weh?'). Also, it has a separate set of grammatical rules (e.g. the genitive case is much more established).
Some German dialects favour the use of articles for people's names (e.g. 'Da Peter hot ...' in Bavarian) whereas in High German, articles are not used before names.
Nevertheless even in Hochdeutsch you can use past perfect instead of preterite to talk about the past. Pekka and I agree that the Frontal 21 initial speaker speaks a very clear form of Hochdeutsch.
What you hear on TV comes close to Standard German but has a lot of 'grinding' (Einschleifungen) as the mentioned shortening of 'es' after many verbs. A keen listener will get a good grasp of it after watching some of these videos (although their content is very bad quality in my opinion).
Perception of Hochdeutsch
When speaking Hochdeutsch as I do, nobody is able to tell where you come from and you are often seen as feeling superior. People cannot give examples why they think so (even after hearing only one to two sentences) which is a clear indicator to me that it's based on my Hochdeutsch. It's funny to have heard more different places I might come from than I have actually ever visited. But it's also sad how little many people know about our dialects.
A very interesting thing about the German language are the irregular verbs. Some of them evolved into new regular verbs (backen: 'backte' and 'buk'). The new regular forms come from dialects and slowly change High German. Greater usage of irregular words makes it less possible to deduce your background. People also tend to classify your phrasing as antique. This can be used for emphasizing prestige.
Elements to emphasize prestige
When introducing people in movies who belong to a higher social level, e.g. royals, this language is used. Additionally, script writers tend to use older or less known idioms to emphasize the sophistication.
To enhance the level of education even more Greek and Latin loanwords are used instead of anglicism or native German words, e.g. saying 'Reputation' intstead of 'Ruf'. Another tool is to add more military speech (royals usually had a military education): to characterize an Austrian royalty you could use "Stellen Sie Ihre Adjustierung her" instead of "Ziehen Sie sich etwas ordentlich an". You only have an Adjustierung if you're properly dressed.