I have a 3 core HP laptop running windows 7, and I don't want windows 7 anymore, nor any of the mess of running a dual boot system. Can I just replace my HD and install Ubuntu and expect it to work? Will my wifi work with a different operating system than the one designed for this machine?
Yes you can replace Win 7 with Ubuntu(I did on the computer I'm using to type this). Everything is likely to work. The wireless may be the exception, they have the tendencies to give you the most trouble but many work flawlessly.
The easiest way to see if how your laptop will work is to boot from a LiveUSB/DVD.
The Live media will run slightly slower than a full install but it will allow you to test your hardware.
The other option is to install inside Windows with Wubi and create a virtual install inside Windows. Again this will run slower than a full install but will allow you to test your hardware.
Any of the option I listed will require you to download the ISO file from here.
You can also check to see if you laptop is listed as Certified. Certified hardware has been tested and will run as if Ubuntu was the native OS. To check the whole laptop here and to check for your wireless or any other specific component go here.
99% is that your newly installed Ubuntu will not create any wireless access problem. But in order to save your time you can just try to find out (google it, or check the compatibility lists as it was recommended in the first answer) - does your laptop WI-FI module supported by Ubuntu.
Some times several type of WI-FI modules are perfectly work under windows but has a problem with linux (for ex., I had a problem with Ubuntu 11 + nc6000 + some broadcom based chipset WI-FI card compatibility)
Also as I remember Ubuntu has an option to start a virtual kind of installation in "test, trail" mode, when you are not going to change or delete your HDD content - but you can basically check the Ubuntu functionality and make some kind of your possible new OS review, maybe it's another chance to check your wifi question.
PS: Finally, if your Laptop's wi-fi module in not currently supported by Ubuntu - you can always replace the card to another one. HW replacement procedure is extremely easy. The cost of new compatible wi-fi card will be not more than 10-15USD. But always remember that you will save hundred's because of no permanent payment to Microsoft for every new windows release.
You should have no problems at all running Ubuntu on your machine. I have Ubuntu on both my desktop and laptop machines. In both of my machines there was no problem with the wireless. However if you do experience any issues you will most likely find the answer here on askubuntu.
Here is the exact link on the [ubuntu website] for the live cd download page.