Uncommon requests during job interview negotiations I'm curious about how common it is to negotiate for requests/demands that are not necessarily directly related to salary, research, or teaching load during the job hiring process in academia. 

Some potential examples that come to mind:


Coverage of school athletic facility fees
Parking pass / daily commute costs (e.g., bus fare)
Financial assistance for relocating for job
Specific holidays (e.g., lesser-known religious days)
Keys to restricted areas not pertinent to job (e.g., access to music rooms for the professor that used to be an active musician)
Coverage for continued learning in unrelated field (e.g., philosophy or theology courses offered elsewhere in the college). 
Others...


Further, is it advantageous to even negotiate for these requests? Has anyone in the SE community had success with similar requests?
There are a lot of perks that come with being an employee of a university, so it may not be necessary to make a lot of the requests for the items you've listed above. For instance, many universities (where possible) subsidize public transportation or parking costs for their employees in an attempt to be environmentally friendly (and reduce the need for on-campus parking). Similarly, there may be programs in place that offer reduced or no tuition for "continuing education." And certainly relocation expenses are not unusual in job negotiations (I'd even argue those are standard for anything above a postdoc, and even for some postdocs, depending on the employer).

However, the more unusual your request—the key access to music practice rooms, for instance—the less likely I'd want to bring it up during job negotiations. It's just too unlikely to get anywhere, and you don't want to get off to a bad start in the process. That said, that doesn't mean you can't inquire about such things after you've accepted the offer.