As the others have already pointed out, yes, Windows 7 will do an "in-place" upgrade, as MS calls it. This is also known as a "dirty" upgrade.... for a reason.
If problems occur down the road with a "dirty" upgrade, there will always be that nagging suspicion, "Is this a real Windows 7 problem or is it caused by some conflict left over from the Vista install?".
So yes it can be done, I have done some myself in the past (98-XP, XP-Vista) but doing it successfully requires:
a) The BIOS and Chipset need to reviewed for compatibility and updated as needed.
b) EVERY other driver must be reviewed for compatibility and updated as necessary.
c) Each and every application should be reviewed. Though you can just "let 'er rip" and discover which ones fail after the upgrade, the danger lies in that some software MUST be uninstalled BEFORE the upgrade for a successful re-install after the upgrade.
d) Before the upgrade, clean the registry, defrag the disk and backup the system IMAGE.
So yes, it can be done, but after doing all of the above it is not that much more work, and sometimes less, to do a clean install.
And you won't be left with that nagging "Is this a real Windows 7 problem or is it caused by some conflict left over from the Vista install?".
Bewarned that, and I tell my clients this, you may (will) lose some of the OEM bells and whistles apps that companies like Dell and HP include in an OEM configurations. But most of those were uneeded to begin with and often the client does not even know they were there (Dell Support, etc, etc). Also, people will have often LOST the 3rd party apps' installation CDs and license keys that came with the original PC (Roxio, PowerDVD, etc). Sometimes the Product Keys can be retrieved with apps like Belarc Advisor, etc. But the OEM installation CD is still needed.
So, in short...... I suggest you do a clean install. It takes a lot of work to ensure a successfull dirty upgrade.
Personally, I am anticipating an abundance of new clients/work in the near future from Windows 7 Upgrades. The smarter (unskilled) users will come to me for help before they do the upgrade. The others will come to me for help after they do the upgrade. I charge the same rate either way....