But what are you counting as an obscure peripheral?
I've had problems with a Pinnacle PCI video capture card, but to be fair, there was no post XP drivers for that anyway.
And a slide scanner. Ditto, no XP drivers, and Linux support patchy, but I can run XP in VirtualBox to access it over USB.
I did also have some problems with a broadcom wireless chipset from around 2001, but it would not work with WPA in XP, even using the available Windows drivers.
But graphic cards? The open source nvidia and ati drivers work well (at least for 2D) with most old hardware, in fact much better than the legacy Windows ones once the proprietary windows ones have dropped all support. And the open source 3D support is getting better all the time, and for reasonably current hardware the binary non-free drivers actually work very well. There was some criticism of multi-head support, but it does work, although maybe not as easily as Windows, and again, it's getting better all the time.
Similarly sound, network, wireless, USB devices. I have far more problems with Windows drivers rebuilding older machines than I do for Linux.
Generally for older hardware, if someone wrote a Linux driver for it at some time in the past, it's still there and probably still in the repositories and the module stubs are still in the kernel, unlike Windows, where the old drivers more often than not will not work at all.
One word of caution for people with older Celeron, some Atom and some Mobile Pentium processors (like the Banias Pentium M that was put in many laptops in the early noughties) that either do not support PAE (Pentium Address Extension) or report it wrongly. Modern Linux distro's often do not come with kernels that support these systems. It is sometimes possible to work around this, but generally it's not worth the effort.