For a more formal tone:
* Typically
* Usually
* Ordinarily
* Customarily
* As a rule
For a more informal tone:
* Mostly
* For the most part
* In most cases
* On average
* By and large
For a more specific emphasis on the majority:
* Predominantly
* Primarily
* Widely
For a more neutral tone:
* Commonly
* Frequently
* Often
It's important to consider the context of the sentence and the desired effect when choosing a synonym for "generally."