It works fine here on a Mac with CS 4 on OS 10.6.2 I have video that shows it works as expected if you woud like to see it.
I think if we knew whatt version of AI you are using and what system we could tell you how to reset the preferences.
here is a screenshot of my settings but I do not think that is the problem.
To reset the preferences the quick way is to hold down the Command Option Shift keys on the Mac when launching AI you hold the keys down firs and keep them held until launched on the PC hold the Alt Control Shift r trash and or move the Adobe Illustrator Settings folder in the users prefernces on a Mac and in Documents and Settings on the PC, I thin. some one will come along to give yu better windos instructions.
Check the zoom level. Snapping is tied to the magnification and thus effectively is dependent on what pixel data is used for the preview. 100% is recommended. Usually, at 200% zoom things level off, though. Zooming in further then does not seem to influence snapping any more.
At 300% on the Mac it works fine here no problems?
Sorry it took so long to reply! Zooming to 100% and even 300% didn't work (i'm on CS3 by the way), but actually I think once the obbject is pasted, if you nudge it to the grid using the arrow keys that seems to work and it then picks up where it should lie.
Thanks for your help anyway!