I think I may have the solution, as I have just experienced this same issue and resolved it.
But first, I have to say to some of the posters in this thread - grow up. Just because you have never heard of or experienced the same problem as someone else does not mean they are not experiencing it. If all you have to offer is criticism and berating someone then don't reply at all.
My issue was with my iphone and started the other day when I was moving things into folders on the phone. One of my folders suddenly disappeared and so I did a reset/restart hoping to recover it. Instead, when my phone rebooted ALL of my folders were gone leaving me eleven (11) full pages of individual Apps, all listed alphabetically. Everything after "s" was gone. I still don't know what happened there.
The next day I tried to add a homescreen link, as I often do for frequent sites, and the option was missing, just like posted here. I tried everything I could think of and nothing worked. In the process of moving around apps from my toolbar to a page an app was bumped off the end. When I replaced the app into the toolbar it left an open space. It dawned on me that maybe I couldn't add a homescreen link because all of my pages were full, apparently eleven is the max on an iPhone 4. Sure enough, when I went back to set my link the "Add to Homescreen" option had returned and worked as it always had.
Is it possible that those of you experiencing this issue with your iPhones/iPads have maxed out all of your homescreen space with Apps? If so, try deleting an app, or put apps into folders to make room and then try and create a new homepage link and see if the option has returned. If this is not the case, then I have no other idea as to what could be causing your particular issue.
Good luck