Yup. Missing ";"s will get you every time.
You might want to look at Komodo from ActiveState. Komodo's an editor that lays code out for you, and pre-empts the function name while you're typing.
For instance, if you type "mysql_q" it will know you're looking for mysql_query. It will make your job easier.
And there's a free version!
I would also separate the sql from the query. It will make your code easier to read, and deliver some functionality down the track when you step up a level in your scripting.
So instead of your example above, I would make it
$query = "INSERT INTO users (Username, Password, Email)
VALUES ('abc', '123123', 'firstname.lastname@example.org')";
$result = mysql_query($query, $link);
The other suggestion is to get into the habit of specifying your link, that is, ($query, $link) instead of just ($query).
At the moment, you're probably using a single data file, but mySQL allows you to use many, each specified with a different link. As your application grows (it will) and you add more features (you will), it will save you the trouble of having to go back and rework your queries.