Also, where can I find the most and least common majors for certain colleges? I am, of course, not looking to try and “game the system” by applying under one major, getting accepted to a top university, then switching majors. I am, however, curious if this changes anything. I want to apply as a computer engineering and/or computer hardware engineering major (as this is my desired field of study) however I believe that I may have a more desirable resume if I were to apply to careers as a computer science major with a minor in electrical engineering or vice versa. If applying as a more focused, probably less common major like computer hardware engineering would aid my chance of application to selective colleges (Stanford, Berkeley, MiT, etc.) then I feel it may be worth it to apply for the more specialized field. If the more general fields mentioned previously would aid my chance of getting a career as well as not hurt my chance of getting accepted that may be more worthwhile. So, how does this all impact my likelihood of getting into these top schools? Or does it not? Thanks 
To answer your question on admissions chance…it depends on the school. Some schools don’t allow you to declare a major until 2nd year. Others ask your intentions during admission. You’ll need to research each of your target schools to determine the answer. More info: http://www.collegeconfidential.com/dean/000062/
Common majors can be deduced by examining the Degrees Conferred, which is included in the Common Data Set each school publishes. I haven’t seen a good site to easily explore this data set, but a search for + “degrees conferred” will likely find results. Example:
https://registrar.stanford.edu/everyone/degrees-conferred/degrees-conferred-2015-16#bachelors
Very much appreciated, thank you 
Also consider that at some schools changing majors is very difficult or involves applying as if you are starting over - Berkeley may be one of those with several majors “impacted” and thus difficult to get into as a first year and maybe impossible later.
College Raptor (■■■■■■■■■■■■■■■■■) does a pretty good job at this.
For a particular school, you can see a list of majors, number of students (and percentage relative to the total student body) graduating with that major, as well as #/% male/female.
For a particular major, it will list the schools that offer that major and the number of students (and percentage relative to the total student body) who have graduated with that major.