Hello!
I'm also a beginner in Vietnamese but I think I can answer your question.
First of all, the North accent (as spoken in Hanoi) and the South accent (as spoken in Saigon) are the most popular. However, there are many other accents thorough out Vietnam, and if you go look the wikipedia page about Vietnamese (
http://en.wikipedia.org/wiki/Vietnamese_language) they give 5 category of ways the tones are spoken in the country.
Not only tones are different, but also some of the words, like Oanhle wrote, from a place to another.
The beginning consonants and the final consonants are also differently spoken from a place to another. For example: the letter "s" in standard pronunciation is like a "sh" as in "shampoo", but in the north they pronounce it like "s" and some places in the south too. Furthermore, depending of the vowel in a word, the final consonant may be pronounced differently as well. Example: "Anh". In the standard pronunciation, the final consonant is like a "ng" of "song" in English, while in the south, it's like an "n", so like "an".
So tones, letter pronunciation (the consonants) and words may differ from a place to another, I will no go as far as say that the grammar is different also, perhaps a native speaker could give more information about that.
For learning Vietnamese, I would recommend you to buy a book with audio that gives a complete explanation about those differences. I started with free online materials but it wasn't sufficient. I'm using the Assimil book series.
Good luck!