I was talking to a native German speaker and he tends to introduce himself like this:
Ich bin der Philipp.
Why "der"?
As mentioned in another answer, it is more common in the South to add the article whereas people in Northern Germany rather leave it out. I live in Western Germany and I use the article, too.
I want to add some further thoughts. I'll reuse the example for that purpose.
Das gehört dem Alex.
Suppose, there is a group of people with more than one person being called Alex and you point at one of them and say that sentence. By that, you kinda put emphasize on whom exactly it belongs.
But note in your question's example it is a bit odd as the following excerpt highlights:
"Hallo, ich bin der Daniel", sagte Daniel. "Und du bist die Barbara, stimmt's?" Die Reaktion fiel nicht ganz so euphorisch aus, wie Daniel erhofft hatte. "Ich heiße Barbara!", stellte die Angesprochene richtig, "ob ich die Barbara bin, hängt davon ab, was du dir unter der Barbara vorstellst. Es gibt allein in dieser Stadt mehrere hundert verschiedene Barbaras. Um sicher zu sein, dass ich die eine bestimmte bin, die dir vorschwebte, als du mich ansprachst, müsste ich wissen, wie du die Barbara definierst!" SPIEGEL
In the Alex-example you can also differentiate between two people with different sex but same name (Alexandra, Alexander).
Das gehört der Alex(andra).
In addition to that another excerpt:
[...] Es sei denn, man ist in einer Kita, einer Kindertagesstätte. Dort wird jedes Kind mit einem "der" oder "die" versehen. Dies macht es den Kindergärtnerinnen leichter, sich das jeweilige Geschlecht ihrer Schützlinge zu merken. Bei Vornamen wie Eike, Kim, Dominique, Marian, Kersten, Elia, Yael oder Sidney ist schließlich nicht für jeden gleich ersichtlich, ob sich dahinter ein Junge oder ein Mädchen verbirgt. [...] SPIEGEL
Some people won't like it if you add a die in front of their name (or leave out):
(Die) Diana vs (Die) Jana
(Die) Diana vs (Die) Anna
"Es heißt nicht die Jana, sondern einfach nur Jana." SPIEGEL
Denn wenn sie sich als "Diana" vorstellt, verändert das bayerische Ohr das automatisch in "die Anna". SPIEGEL
Just for your information: In some regions female person are neuter ;p
Im Rheinland und Umgebung werden Frauennamen traditionell mit dem bestimmten sächlichen Artikel ("dat") versehen: dat Gerda, dat Uschi, dat Chantal. SPIEGEL
Of course, if someone introduces himself, it should be (but not always ;-) obvious which gender is appropriate - but here it's something regional, if one uses the article when speaking of ones name.
This difference occurs even more clearly when speaking about someone, so for example you can say
Das gehört Alex. Kommt Alex heute mit?
or
Das gehört dem Alex. Kommt der Alex heute mit?
I personnaly use the latter form, but you'll find both versions.
On a not-able-to-show-references basis, I would say that using the article is more common in the south; not using it, in the north of Germany.
Geziefer and Em1 are right - it's primarily a North-South thing.
In my experience this has little to do with real practical reasons - the clarification thing Em1 mentions feels like something entirely different to me (it also is always characterized by a strong emphasis on the article which isn't there in the usage you're referring to, Gigili).
Another distinction is a social rather than geographical one: there's a stereotype that overly PC and socially/ecologically conscious people talk like that (cf. "Ich bin der Martin, ne?".
Also, it appears to be a feature of kiddie-talk: "Das sag ich dem Papa!" (a threat to tell Daddy about something) sounds much more stereotypical (and 'younger') than "Das sag ich Papa!"
(Educators - at least according to the stereotype - fall in both categories :))
MAIN POINTS
As everyone has remarked, as far as informal speech is concerned, it is a matter of difference between North and South - where Southerners are the ones to add articles. Having lived in the South for the last 13 years, I have started to acquire it myself.
There can, however be little doubt, that German Standard German does not allow this usage, as I can not come up with any example where this was used in classic German literature. I will now start a search in the works of Austrian writers Zweig and Doderer, though Ingmar has already provided evidence of "extra" articles in works of other Austrian writers.
TITLES AND GENITIVE
Several comments have shown people confuse this issue with articles in front of titles. This must be treated separately. For instance, it is totally acceptable, even in the North, to write:
Im Hause des Herrn Lunte wurde Sonntags stets Grütze gegessen.
Die Studienrätin Ludmilla, die Nichte des Herrn Rustikov und Tante des Johannis war eine strenge Frau, welche nichts mehr ergötzte, als die blanke Furcht ihrer Schüler.
Here "des Johannis" is preferred to avoid antiquated genitive forms such as "Johanisens". Through, I think, we should not drag the genitive into this. I believe it is always permitted to form it with des, just usually not preferred.
With titles, care has to be taken. In Standard German German you should observe, how strongly the title forms part of the name.
Ich kenne Herrn von Ilmenstein seit Jahren = I have known Lord Ilmenstein for years
But:
Ich kenne den Herrn von Ilmenstein seit Jahren =I have known the lord (and Master) of Ilmenstein for years.
Said master may in fact not be Lord Ilmenstein, but rather an usurper named Björn Malte Mehring-Brunnendreck.
Furthermore, confusion has arisen in the comments concerning cases like ministers, prime ministers and so on. Since these are unique, when not followed by a name, they demand articles:
Der Aussenminister gab einen kurzen Bericht.
Additionally, we use articles in front of occupations to convey additional meaning:
Der Lehrer Strack wusste, wie mit ungezogenen Jungen zu verfahren war.
Der Physiker Dimpfelberger hatte keine Angst vor der Atomenergie.
These are variants of:
Dimpfelberger, ein Physiker, hatte keine Angst vor der Atomenergie.
AUSTRIAN GERMAN
EDIT: Ingmar has already provided examples of Austrian writers using the "extra" article. The clearest one is from a work of Jörg Mauthe "vom Thomas begleitet streife ich durch die Ruine...". Naturally, works that want to convey a particularly Austrian setting are full of this. For instance "Die Tante Jolesch" by Torberg.
SEMANTIC ISSUES
Other answers have not yet highlighted the benefits of including the article for clarifying some ambiguous sentences. The sentence:
Der Tom hat den Richard geschubst, nicht den Martin
is unambiguous, however:
Tom hat Richard geschubst, nicht Martin ,
remains ambiguous!
That is not to strongly argue for the inclusion of the article, since the slightest syntactic awareness clarifies every misunderstanding, by opting for :
Tom hat Richard, nicht Martin, geschubst,
or
Tom, nicht Martin, hat Richard geschubst.
Bastian Stick points out the semantic difference between "Barbara" and "die Barbara", the latter being a specific one. While that is usually sufficiently clear by intonation, please refer to my earlier example, on the Lord of Ilmenstein, where no Intonation will save you. This obviously concerns marginal cases, so it's no big asset of standard usage either. A further example would be:
Frau Bartels = Mrs Bartels
die Frau Bartels = Bartels Frau
But here, luckily, intonation suffices to clarify the meaning of colloquial usage. "Frau" as a title is stressed very little. And, even in the North, "Bartels Frau" is the common genitive. You could, however, create such sentences for the joy of it:
Beständig drehte sich Bartel, welcher sich unbeobachtet wähnte, nach der attraktiven Frau Bartels um. Doch ließ die Frau Bartels, Frau Bartel, Bartel Bartels betrachten, wollte sie doch erforschen, wie dieser sich in ihrer Abwesenheit verhielt!
Perhaps, Indoeuropean languages tend to develop in this way. I find the inclusion of the article more and more often everywhere in Germany. It might be that speakers consider the Tom-Richard-Martin clarification a virtue. Note, however, that Greek, which inflects names and thus does not need such clarification, has also developed from a stage where omission of the article was allowed to mandatory inclusion!
Just wanted to add: I live in west Germany and I know many people who say this (including myself). So I wouldn't say that this is not common here.
In this context, it is added for emphasis.
"Ich bin der Philipp," translates into "I am the Philipp." (Not just a "random" Philipp.)
It connotes a sense of self-importance. although some Germans use it, this is not standard usage. It is best used for important people like Presidents (perhaps even of a company), that is the "big boss".
It is appropriate if someone happens to be the (wo)"man of the moment." For instance, if "Philipp" just published a best-selling book, or even a book, it might make sense to call him der Philipp for a period of time.
Just my two cents here of a German native speaker well aware of good German but not professional concerned with language:
Concerning the "der" vs. "der Philip" I would "der" just classify as a special emphasis in spoken context, I see myself less a north-south gradient here as a question if I want to emphasize my name. When twenty people tell each other their names, I would add only "Philip" or
"Ich bin Philip"
whereas when I want more attention I could add a der.
It is worth to say that "Ich bin ..." is in less cases the common form of introduction or naming himself than in English. In German "Ich heiße" oder "Mein Name ist" is traditionally more common.
"I am Joseph Pulitzer, and you are hearing AM news."
would be not translated into proper German with
"Ich bin Joseph Pulitzer.."
but
"Ich heiße Joseph Pulitzer.."
despite the trend to use English constructions in German sentences.
When introducing himself to a larger audience, it is more proper to say:
"Mein Name ist Joseph Pulitzer."
(or "Ich heiße") instead of "Ich bin Joseph Pulitzer."