Windows 7: Using old HDD with copy of Windows 7 in new PC

I am planning a build for a new pc and budgeting heavily. I was wondering whether it is viable/safe to put my HDD from my old PC into a totally new pc. Would it just run normally, or is there something i should do, say to get Windows to recognise the new hardware? Or would it just not work?
I would wipe the HDD and reinstall Windows, but I did not recieve the Windows Install disk with my store-bought pc and i don't feel like buying another copy of Win 7.
I'm open to suggestions.

If the old PC came with preinstalled Windows 7 then you can reinstall it as often as you want and in any way you want for the life of the PC. Everything you need is here: Clean Reinstall - Factory OEM Windows 7

Unless you want to move a Retail Windows 7 from old to new, you'll have to buy a new copy of Windows 7 for the new build, but you can get a price break on System Builder OEM.

If the current OS is the same version and the moved HD won't start on the new PC, move it back to the old hardware to SysPrep to move HD to another computer. Then after it starts up and changes out all the drivers, change the Product Key to the newly purchased OEM copy in Control Panel>System.

Thanks i'll see how i go.