Aeismail makes an important point about location: what's standard in Germany differs from what's standard in the US.
In a US context, I would strongly recommend against listing things like declined graduate fellowships. It will look strange, and even beyond that it can work to your disadvantage: everybody will already assume you declined several attractive offers, so giving an explicit list will do nothing but focus attention on what isn't on the list. (If the list of declined offers is short, readers will be disappointed, and if it's long, they'll spend more time speculating about what's missing than being impressed.)
The only time I'd recommend highlighting this sort of information is if for some reason you had to turn down a vastly more prestigious offer than the one you accepted. For example, maybe you were offered a tenure-track job at a top department, but ended up working as an adjunct in the middle of nowhere so you could take care of a relative. You should then make sure everybody knows this the next time you are able to apply for jobs. However, you should be very careful when doing this, because if the prestige difference isn't absolutely universally acknowledged, then you run the risk of offending people who feel you are unfairly denigrating a perfectly fine career path.