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Use consistent code formatting

Right now, you have several lines of code with different indentations, spacing, etc. You should pick a single spacing style and stick with it for the entirety of your program to improve readability.

while(i == word.length()) 

 System.out.println("The number of vowels is: " + iterations);
 System.out.println("The total sum of all vowels is: " + totalValueOfVowels);
 break;

 

Here, for example, your closing curly brace does not line up with the beginning of the while loop. Similarly,

else 
 System.out.println("This isn't a vowel: " + word.charAt(i));
 System.out.println("------------------------");

Your else statement has a space after it, but not before.

It generally doesn't matter what coding style you choose, as long as you do choose one and stick with it.

Initialize variables at the first point of use

Variables should be initialized as closely to where they are used as possible. For example, your scan variable is only used in your main method, so it should be initialized there.

public static void main(String args) 
 Scanner scan = new Scanner(System.in);
 ...

Do the same for the rest of your variables. All the rest of them (except for word) are only used in the counter method, so they should be initialized there, as close to their first point of use as possible.

word is initialized in main and then used in counter, so it should be passed in to counter as an argument.

public static void counter(String word) 
 ....


public static void main(String args) 
 Scanner scan = new Scanner(System.in);
 String word = scan.next();
 scan.close();
 counter(word);

As you can see, we can pass word as an argument to counter.

Simplify your call to counter

The above snippet also addresses another issue - the counter method is only called from main, which means you can make it a static method. This way, we do not have to initialize a new vowelCounter just to call the counter method - we can freely call it from main.

If you really wanted to make counter a non-static method, then I would suggest moving it to a different class than your main method. Then, you can create an instance of that class and call the counter method on it. In general, creating a new instance of the class that contains your main method is a strange pattern and should be avoided.

Simplify your for-loop

In general, a variable used as a counter in a for-loop should be initialized and incremented within that for-loop statement itself. To accomplish this, you would want to remove the int i and the lines that call i++;, and format your for-loop as follows:

for (int i = 0; i < word.length(); i++) 
 ...

However, there is an even better way to express our intent of "loop over all characters in a String". We can format our for-loop into a foreach-loop as follows:

for (char vowel : word) 
 ...

Now, we can remove the line vowel = word.charAt(i), since vowel will now automatically loop over every character in the given word.