YSK that if you apply to transfer from your current university to a new one, your new school will probably want to see the syllabi for all the courses that you've already taken.

I know this from experience - your new school may want to see all of the syllabi for the courses you took at your old school, in order to determine equivalency of courses and to make determinations about transferring credits.

So, even if you think you maybe might want to transfer at some point down the line, save all of your syllabi, because you might need them in the future.