I know in many of the science fields, a PhD student will receive a stipend for being a teaching assistant while earning his/her degree. Does this happen with other fields, such as History? Are there specific universities that are more known to pay these non-science PhD students?
Assistantships and fellowships are offered in all types of PhD programs, the disparity is in the number of funded positions a given department or field will have and the level of support offered. For example, a given engineering professor might be able to offer full tuition and a$30k stipend to two PhD candidates while their peer in history might only be able to offer in-state tuition* and a $15k stipend to a single PhD candidate.
As to which history programs offer more or better support, I really cannot comment, not being in that field. Generally speaking, this is not especially relevant in applications anyway because almost every department will have some money, and it is all but impossible to know your own standing amongst the admitted cohort prior to actual notification. In other words, apply to a spread of departments where you have a real interest, and expect to decide between a “better” department with less or no support and a “lesser” department with better support.
**: Meaning that out-of-state grad students would still be liable for the remainder. *
Broadly speaking, yes. Social science and humanities PhDs are usually offered full funding packages as well, although on average the funding is less than it would be for the STEM fields. Amounts of ~$30K are pretty common in the sciences; in the humanities, I would say that the amounts are generally about $18-25K, whereas in the social sciences it might be more like $22-30K. (I am in a social science, and my stipend was $32K.)
Generally speaking, the top/best programs in a field also offer the best stipends. However, remember not to compare absolute numbers but cost of living. $27K might go a lot farther in West Lafayette than $32K does in San Francisco. Also, remember that your doctoral days are a but a short period of your life and it pays to be frugal if it means going to a better program for you. (However, I will say that you shouldn’t accept a place in a program that pays less than you could reasonably live on.)