I find it odd for people to specifically request that we bring something (other than in a potluck situation, of course) but I don't really mind.
On the other hand.. my niece throws big family gathering parties and plays up how much work she's putting into it when what she does it to cook say, a large turkey, and that's it. She invites people and makes a HUGE deal of getting them to RSVP right away (on facebook, mind you) and when they do, she specifies exactly what they are to bring, how much, using what recipe, or exactly where to buy it.
For example, earlier this spring she hosted one of these events and when DH responded that he would be able to attend, she told him to go buy two $30 cakes from a specific bakery (no where near his house, or hers- it was a 45 minute drive out of the way) for people to have for dinner. I found that pretty over the top.
I think it's nice when getting together for family stuff especially to respond to inquiries about what to bring with something general along the lines of, "everyone always LOVES your salads- that would be a great treat!" or "Well, this is what I've planned, is there anything you'd like to bring with you?" In my family, that's often done (with NO pressure, it would be ok to show up without anything) to have fun coordinating a meal. Aunt Sue is bringing her wonderful peppermint chocolate bars, Jane is bringing that salad she made last time we were there, and Uncle Dave is making his famous dip... but it's never an expectation.
As for us, I will usually try to suggest I bring something I know my kids will eat. I have really picky kids, so that can be an issue and I like to know we'll work around it.