It's not just that the average PC sold today has more than enough memory or horsepower, but Microsoft did hard work to make 7 more efficient and responsive. Many of these changes may not be obvious to the casual user at first -- they're "under the hood,"not flashy user-experience items -- but they do add up.
My Lenovo S10 Ideapad netbook, an Intel Atom-powered machine with 1GB RAM, is nobody's idea of a speed demon. But Windows 7 installed on it without a hitch, kept at least 500MB RAM free with no other processes running, and made good use of the screen despite the cramped display size.
With Linux, each distribution has widely varying hardware requirements, which is exactly the idea. No two distributions are meant to be alike; they all serve different needs and user requirements. That said, the top few (Ubuntu, Fedora/Red Hat, openSUSE, Debian) usually do the trick, either by themselves or through one of their derivate editions (e.g., Xubuntu for Ubuntu on systems with minimal hardware).
In every case, you can always determine if your hardware is supported in Linux by simply burning and booting the live-media .ISO for a distribution: If it works, you'll know almost immediately.
Hardware And 64-bit Driver Issues
The rule of thumb for hardware running Windows 7 is this: if it worked with Windows before, it should work now. There is, however, one caveat: 32-vs.-64-bit.
The computing world's been tilting towards 64-bitness for some time now. Servers, full-blown desktops, and high-end notebooks are going 64-bit, while netbooks and more modest machines will stick with being 32-bit. That said, there's not a lot of immediate pressure to move to 64-bit if you're not already there, and neither the newest versions of Windows, nor Linux will change that.
A major reason for this is that most hardware manufacturers are only now habitually supporting 64-bit Windows for newer devices. It's the folks who have older or more slightly off-the-beaten-path peripherals -- host-based printers, scanners, or multifunction devices; Web cameras; wireless devices; and pro-audio sound cards -- who will run into trouble.
But because the nature of hardware support is so different in Windows and Linux, the amount of hardware supported on each might be a factor if you're planning on running 64-bit.
In Windows, device drivers are generally closed-source, proprietary items; they're provided by the hardware manufacturer or by Microsoft directly. In Linux, though, the majority of hardware drivers are open-source; only a small handful of devices run on proprietary drivers.