He's special in that he was the first dictator born to the name of 'Caesar'. Taking his name was a means of establishing your legitimacy as father of the country and descendant of Venus, which was a strategy first employed by his adopted son, Octavian (later Augustus). Most Roman 'emperors' (the term is a retrospective one, for the most part) would have been referred to and addressed as 'Caesar', for example in Vitruvius' dedication of de Architectura to Octavian ( http://penelope.uchicago.edu/Thayer/E/Roman/Texts/Vitruvius/1*.html ). This later dedication to Trajan, as you can see, has the name 'Caesar' right at the top ( https://farm3.static.flickr.com/2325/2152955926_6a298e7a98.jpg ).

Caesar is 'arguably the most famous emperor of Rome' because he's commonly received as having put paid to the Roman Republic and catalysed the age of rule-by-dynasty. It helps that his life was highly dramatic, involving a life on the run from Sulla and extensive military conquests, ending with a grisly murder in the heart of the eternal city, immortalised in countless plays, paintings and other media. In my opinion this is a bit too much at the expense of Sulla who was probably equally as important as Caesar, if not more so, in precipitating the crumbling of the Republic but that's for another thread I guess.

This subject is complicated because a) the Romans had lots of names b) these names changed during their lifetime (usually after adoptions). c) Historians use shortened versions in order to easily delineate between them BUT this doesn't reflect the name reality for the person at the time. So, to add to what /u/Juvenalis has said. You have to be wary in the titles used to refer to the Roman leaders, especially after Augustus. First and foremost among these is the word 'Emperor.' We use various titles and names to characterise the leaders of the Roman world but these would not necessarily derive from the ancient, contemporary political titles for instance out word 'Emperor' derives from the Latin Imperator which was originally a Republican accolade shouted by troops to a particularly successful and popular general at the end of a battle. Imperator was then incorporated into the titles.

On the question of Caesar, the original usage was indeed for Gaius Julius Caesar who was assassinated in 44BC. But Roman names are far more fluid than many modern equivalents. Thus, when Octavius was adopted posthumously by Caesar he became Gaius Julius Caesar Octanianus. His contemporaries would have refereed to him as Caesar as that was his family name, with close friends perhaps calling him Gaius. He then was granted the title Augustus in 27 BC, which historians use to designate him apart from the other emperors. Augustus actually designated himself the title Princeps meaning first among equals continuing to maintain a facade of the titles used in the Res Publica (Republic). But, this does not mean that other later emperors did not also use the titles 'Augustus' 'Caesar' among many others (see the example used by Trajan (the IMP. is an abbreviation of Imperator)

Also, you should bear in mind that Julius Caesar is not considered the first emperor. He was certainly consul and designated 'dictator for life' and (had he not been assassinated on the Ides of March he may have become something akin to an emperor).

So to answer your question more succinctly: Caesar refers now to Julius Caesar because that is the term modern historians use, but did not necessarily reflect the contemporary name situation in ancient Rome. Google has yet to develop the technology for detailed historical analyais (although give Google scholar a shot and you'll get some good literature on the subject). Therefore when you search for 'Caesar' the search results will be based on the modern historians name designations. Lastly, Caesar was indeed a remarkable historical figure and the reason we see him as famous is that so many ancient sources wrote about him. Check out Plutarch's Parallel Lives And Suetonius' Lives of the Caesars

These provide an excellent basis for understanding the Roman Emperors and how they were regarded socially and politically. For some more reading on how Roman names worked try:Imperator Caesar: A Study in Nomenclature Ronald Syme, Historia: Zeitschrift für Alte Geschichte, Bd. 7, H. 2 (Apr., 1958), pp. 172-188

For a lighter read, the Historian Tom Holland wrote a fantastic book dealing with the last years of the Republic that deals with Caesar as well: Rubicon: The Last Years of the Roman Republic by Tom Holland

Last of all Mike Duncan's Podcasts on Caesar and Augustus provide an excellent initial history to the whole of Roman history but particlarly imperial politics.