I have Ubuntu 11.04 & Windows 7 dual-booting on my laptop and I want to upgrade to Ubuntu 12.04.
I'd like to know whether this upgrade will damage my Windows partition. Is it safe to do so and will everything still work correctly afterwards?
If your current dual-boot installation is working properly now, then NO it will not damage your Windows installation when you upgrade.
Note that you'll first have to upgrade to 11.10 and then to 12.04. You won't be able to upgrade straight from 11.04 to 12.04. For additional information the following questions and their answers will be useful:
Alternatively, you can do a clean install of 12.04 over your existing 11.04 installation. That is also possible and you can read up on the advantages of doing so by reading the answers to this question: Is a clean install better than upgrading?