I have a home and work computer, the home computer has a static IP address.

If I ssh from my work computer to my home computer, the ssh connection works but X11 applications are not displayed.

In my /etc/ssh/sshd_config at home:

X11Forwarding yes
X11DisplayOffset 10
X11UseLocalhost yes

At work I have tried the following commands:

xhost + home HOME_IP
ssh -X home
ssh -X HOME_IP
ssh -Y home
ssh -Y HOME_IP

My /etc/ssh/ssh_config at work:

Host *
ForwardX11 yes 
ForwardX11Trusted yes

My ~/.ssh/config at work:

Host home
HostName HOME_IP
User azat
PreferredAuthentications password
ForwardX11 yes

My ~/.Xauthority at work:

-rw------- 1 azat azat 269 Jun  7 11:25 .Xauthority

My ~/.Xauthority at home:

-rw------- 1 azat azat 246 Jun  7 19:03 .Xauthority

But it doesn't work

After I make an ssh connection to home:

$ echo $DISPLAY
localhost:10.0

$ kate
X11 connection rejected because of wrong authentication.
X11 connection rejected because of wrong authentication.
X11 connection rejected because of wrong authentication.
X11 connection rejected because of wrong authentication.
X11 connection rejected because of wrong authentication.
X11 connection rejected because of wrong authentication.
X11 connection rejected because of wrong authentication.
X11 connection rejected because of wrong authentication.
kate: cannot connect to X server localhost:10.0

I use iptables at home, but I've allowed port 22. According to what I've read that's all I need.

UPD. With -vvv

...
debug2: callback start
debug2: x11_get_proto: /usr/bin/xauth  list :0 2>/dev/null
debug1: Requesting X11 forwarding with authentication spoofing.
debug2: channel 1: request x11-req confirm 1
debug2: client_session2_setup: id 1
debug2: fd 3 setting TCP_NODELAY
debug2: channel 1: request pty-req confirm 1
...

When try to launch kate:

debug1: client_input_channel_open: ctype x11 rchan 2 win 65536 max 16384
debug1: client_request_x11: request from 127.0.0.1 55486
debug2: fd 8 setting O_NONBLOCK
debug3: fd 8 is O_NONBLOCK
debug1: channel 2: new [x11]
debug1: confirm x11
debug2: X11 connection uses different authentication protocol.
X11 connection rejected because of wrong authentication.
debug2: X11 rejected 2 i0/o0
debug2: channel 2: read failed
debug2: channel 2: close_read
debug2: channel 2: input open -> drain
debug2: channel 2: ibuf empty
debug2: channel 2: send eof
debug2: channel 2: input drain -> closed
debug2: channel 2: write failed
debug2: channel 2: close_write
debug2: channel 2: output open -> closed
debug2: X11 closed 2 i3/o3
debug2: channel 2: send close
debug2: channel 2: rcvd close
debug2: channel 2: is dead
debug2: channel 2: garbage collecting
debug1: channel 2: free: x11, nchannels 3
debug3: channel 2: status: The following connections are open:
  #1 client-session (t4 r0 i0/0 o0/0 fd 5/6 cc -1)
  #2 x11 (t7 r2 i3/0 o3/0 fd 8/8 cc -1)

# The same as above repeate about 7 times

kate: cannot connect to X server localhost:10.0

UPD2 Please provide your Linux distribution & version number.
Are you using a default GNOME or KDE environment for X or something else you customized yourself?

azat:~$ kded4 -version
Qt: 4.7.4
KDE Development Platform: 4.6.5 (4.6.5)
KDE Daemon: $Id$

Are you invoking ssh directly on a command line from a terminal window?
What terminal are you using? xterm, gnome-terminal, or?
How did you start the terminal running in the X environment? From a menu? Hotkey? or ?

From terminal emulator `yakuake`
Manualy press `Ctrl + N` and write commands

Can you run xeyes from the same terminal window where the ssh -X fails?

`xeyes` - is not installed
But `kate` or another kde app is running

Are you invoking the ssh command as the same user that you're logged into the X session as?
From the same user

UPD3

I also download ssh sources, and using debug2() write why it's report that version is different
It see some cookies, and one of them is empty, another is MIT-MAGIC-COOKIE-1