Any ham device that is USB or RS232 with a sufficiently "open" (aka "documented") interface can be turned into an internet enabled device with a Raspberry Pi. In other words, if you can send and receive ASCII character strings to control the device, you're basically there.
Most RS232 devices (and all that I actually own) run well off of a suitable USB-to-RS232 adapter (they are out there, not expensive).
Devices I am doing this on include: Arduinos, Sainsmart "dry contact switches" (aka relays), and (soon) a USB-controlled switchable USB hub (so I can turn USB devices on and off individually without being in the room).
Devices I will be doing this on include: Green Heron Controllers (bought mine before their ethernet versions became available).
Devices I could do if I could get the protocol information: Alpha 9500. This one probably stays on Windows.
I have also recently obtained a WinKeyer. I probably can have that one on the "Pi" as well.
Beyond direct ham radio usage, I routinely have SAMBA (looks like Windows File Sharing) and LIGHTTPD (Web Serving) on my Pis.
The latter is important: A simple, basic web page will allow me to access and control any RS232/USB device I managed to support from the Pi. This also means the device can be controlled from a phone or a tablet, freeing me from having to control everything from a PC.
The former allows me to have a lot of things in a known location. By today's standards, the SSD on the Pi isn't very big, but as long as you aren't trying to store a lifetime of photos on them, storage in a typical Pi SSD (even 8 GB) is plenty.