Re: linux
Unless it is a mass storage device (camera, sd-card, disk...) usually nothing at all. I can't speak for ubuntu though. Of course it will be logged to system log, but the common user usually doesn't care much about that.
And simple things like serial adapters usually just work out of the box anyway 
An FTDI adapter will create something like this in the syslog:
07/25/11 11:25:08 PM linuxbox kernel [25248.700042] usb 2-4: new full speed USB device number 3 using ohci_hcd
07/25/11 11:25:08 PM linuxbox kernel [25248.928051] usb 2-4: New USB device found, idVendor=0403, idProduct=6001
07/25/11 11:25:08 PM linuxbox kernel [25248.928062] usb 2-4: New USB device strings: Mfr=1, Product=2, SerialNumber=3
07/25/11 11:25:08 PM linuxbox kernel [25248.928069] usb 2-4: Product: FT232R USB UART
07/25/11 11:25:08 PM linuxbox kernel [25248.928075] usb 2-4: Manufacturer: FTDI
07/25/11 11:25:08 PM linuxbox kernel [25248.928079] usb 2-4: SerialNumber: A6007nZC
07/25/11 11:25:08 PM linuxbox mtp-probe checking bus 2, device 3: "/sys/devices/pci0000:00/0000:00:02.0/usb2/2-4"
07/25/11 11:25:08 PM linuxbox mtp-probe bus: 2, device: 3 was not an MTP device
07/25/11 11:25:09 PM linuxbox kernel [25250.009207] usbcore: registered new interface driver usbserial
07/25/11 11:25:09 PM linuxbox kernel [25250.009240] USB Serial support registered for generic
07/25/11 11:25:09 PM linuxbox kernel [25250.009298] usbcore: registered new interface driver usbserial_generic
07/25/11 11:25:09 PM linuxbox kernel [25250.009302] usbserial: USB Serial Driver core
07/25/11 11:25:09 PM linuxbox kernel [25250.036587] USB Serial support registered for FTDI USB Serial Device
07/25/11 11:25:09 PM linuxbox kernel [25250.037636] ftdi_sio 2-4:1.0: FTDI USB Serial Device converter detected
07/25/11 11:25:09 PM linuxbox kernel [25250.037741] usb 2-4: Detected FT232RL
07/25/11 11:25:09 PM linuxbox kernel [25250.037747] usb 2-4: Number of endpoints 2
07/25/11 11:25:09 PM linuxbox kernel [25250.037753] usb 2-4: Endpoint 1 MaxPacketSize 64
07/25/11 11:25:09 PM linuxbox kernel [25250.037758] usb 2-4: Endpoint 2 MaxPacketSize 64
07/25/11 11:25:09 PM linuxbox kernel [25250.037763] usb 2-4: Setting MaxPacketSize 64
07/25/11 11:25:09 PM linuxbox kernel [25250.042236] usb 2-4: FTDI USB Serial Device converter now attached to ttyUSB0
07/25/11 11:25:09 PM linuxbox kernel [25250.042286] usbcore: registered new interface driver ftdi_sio
07/25/11 11:25:09 PM linuxbox kernel [25250.042291] ftdi_sio: v1.6.0:USB FTDI Serial Converters Driver
The relevant files are:
'/var/log/messages' on openSUSE
'/var/log/syslog' on ubuntu (probably debian as well)
They can be viewed in a text console/terminal with (start this before inserting the device!):
sudo tail -f /var/log/syslog
I'm sure there are GUI tools to show this information as well, but they will vary (drastically) between distributions.