I recently bought the Logitech H600 Wireless Headset. When I plug in the USB wireless transmitter, Ubuntu 12.04 LTS crashes.

How does that come and what do you suggest me to do?

Same problem here, as soon as the H600 headset is plugged in 12.04 crashes.

Relevant snip from /var/log/Xorg.failsafe.log is below, complete log can be found as a gist

[  2676.496] (**) Logitech Logitech Wireless Headset: Applying InputClass "evdev keyboard catchall"
[  2676.496] (II) Using input driver 'evdev' for 'Logitech Logitech Wireless Headset'
[  2676.496] (II) Loading /usr/lib/xorg/modules/input/evdev_drv.so
[  2676.496] (**) Logitech Logitech Wireless Headset: always reports core events
[  2676.496] (**) evdev: Logitech Logitech Wireless Headset: Device: "/dev/input/event16"
[  2676.496] (--) evdev: Logitech Logitech Wireless Headset: Vendor 0x46d Product 0xa29
[  2676.496] (--) evdev: Logitech Logitech Wireless Headset: Found absolute axes
[  2676.496] (--) evdev: Logitech Logitech Wireless Headset: Found absolute multitouch axes
[  2676.496] (--) evdev: Logitech Logitech Wireless Headset: Found keys
[  2676.496] (II) evdev: Logitech Logitech Wireless Headset: Configuring as mouse
[  2676.496] (II) evdev: Logitech Logitech Wireless Headset: Configuring as keyboard
[  2676.496] (**) Option "config_info" "udev:/sys/devices/pci0000:00/0000:00:1d.0/usb2/2-1/2-1.2/2-1.2.2/2-1.2.2:1.3/input/input16/event16"
[  2676.496] (II) XINPUT: Adding extended input device "Logitech Logitech Wireless Headset" (type: KEYBOARD, id 10)
[  2676.496] (**) Option "xkb_rules" "evdev"
[  2676.496] (**) Option "xkb_model" "pc105"
[  2676.496] (**) Option "xkb_layout" "us"
[  2676.497] (II) evdev: Logitech Logitech Wireless Headset: initialized for absolute axes.
[  2676.497] 
Backtrace:
[  2676.497] 0: /usr/bin/X (xorg_backtrace+0x37) [0xb7698637]
[  2676.497] 1: /usr/bin/X (0xb7510000+0x18c3ba) [0xb769c3ba]
[  2676.497] 2: (vdso) (__kernel_rt_sigreturn+0x0) [0xb74ed40c]
[  2676.497] 3: /lib/i386-linux-gnu/libc.so.6 (0xb7155000+0x135d32) [0xb728ad32]
[  2676.497] 4: /usr/bin/X (XIChangeDeviceProperty+0x16c) [0xb7630b0c]
[  2676.497] 5: /usr/lib/xorg/modules/input/evdev_drv.so (0xb3f4a000+0x634e) [0xb3f5034e]