Examples being the old level 60 PVP achievements.
I have Knight-Captain on my account, yet I cannot use it unless I play the character who got the achievement, which I really don't. Having the title also enables me to buy the old moggable PVP gear in Netherstorm... only if I play that character.
Same with the tabards of the Argent Dawn and Protector. I have those, yet cannot use them. At all.
Why won't Blizzard make achievements like those account wide? It infuriates me.