If you need to achieve the best possible quality I strongly recommend against using the Clipboard for transferring graphics. Under Windows the clipboard will contain an out-of-date Windows Metafile which is generated with display resolution fidelity! This is the reason why you see jaggies.
Instead, I recommend to Export your graphics as EPS and then import it in your Word document. Note that most scientific journals recommend to provide graphics in the resolution-independent EPS format.
One possible difficulty with EPS is that it does not support transparency. If your graph contains transparent objects you cannot directly Export it as a correct EPS file from Mathematica. I have expanded this topic and provided workarounds in this answer: http://mathematica.stackexchange.com/a/32948/280
If you are not satisfied with EPS, I recommend you to Export your graphics as EMF from Mathematica. EMF supports transparency but it does not support many other features such as CapForm which EPS supports. So EPS is much more reliable than EMF when there is no transparent objects.
If you use VertexColors in your graph (which PDF format supports but Mathematica's Export still does not) or there are other reasons why EPS, EMF and PDF give unsatisfactory results you may consider Rasterizing your graph and Exporting it as PNG with high resolution. This is not always an easy task because Mathematica's Graphics by default is NOT resolution-independent: Ticks and TickLabels by default do not scale with the Graphics! It is huge headache for any Mathematica user for many years and there is still no easy workaround. In the most cases the best way is to Export as PDF from Mathematica and then export the graph from your favorite PDF renderer to PNG. Other workarounds include some pre-processing inside of Mathematica and/or using third-party software.
Here I'll collect some examples of the preprocessing approach which gives small file size without loose of quality (I will update the list with additional references when I'll have time):