"As a rule" is a commonly used phrase that indicates something is typically or generally the case. However, in order to vary your language and make your writing more interesting, it's useful to have a few synonyms in your vocabulary. "Generally speaking" is a good option, which implies that what you are about to say is mostly true. "In most cases" is another alternative, acknowledging that there may be exceptions to what you are saying. "Usually," "typically," and "ordinarily" are all good options as well. Ultimately, using synonyms for "as a rule" allows you to convey the same meaning in different words and adds a touch of diversity to your writing.