Why does Ctrl+Arrow make my terminal switch to a strange mode?

The solution was pretty elegant and simple: editing /etc/inputrc and disabling vi mode.

Here's the renewed inputrc file:

# /etc/inputrc - global inputrc for libreadline
# See readline(3readline) and `info rluserman' for more information.

# Be 8 bit clean.
set input-meta on
set output-meta on

#set editing-mode vi

# To allow the use of 8bit-characters like the german umlauts, uncomment
# the line below. However this makes the meta key not work as a meta key,
# which is annoying to those which don't need to type in 8-bit characters.

# set convert-meta off

# try to enable the application keypad when it is called.  Some systems
# need this to enable the arrow keys.
# set enable-keypad on

# see /usr/share/doc/bash/inputrc.arrows for other codes of arrow keys

# do not bell on tab-completion
# set bell-style none
# set bell-style visible

# some defaults / modifications for the emacs mode
#$if mode=emacs

# allow the use of the Home/End keys
"\e[1~": beginning-of-line
"\e[4~": end-of-line

# allow the use of the Delete/Insert keys
"\e[3~": delete-char
"\e[2~": quoted-insert

# mappings for "page up" and "page down" to step to the beginning/end
# of the history
# "\e[5~": beginning-of-history
# "\e[6~": end-of-history

# alternate mappings for "page up" and "page down" to search the history
# "\e[5~": history-search-backward
# "\e[6~": history-search-forward

# mappings for Ctrl-left-arrow and Ctrl-right-arrow for word moving
"\e[1;5C": forward-word
"\e[1;5D": backward-word
"\e[5C": forward-word
"\e[5D": backward-word
"\e\e[C": forward-word
"\e\e[D": backward-word

$if term=rxvt
"\e[8~": end-of-line
"\eOc": forward-word
"\eOd": backward-word
$endif

# for non RH/Debian xterm, can't hurt for RH/Debian xterm
# "\eOH": beginning-of-line
# "\eOF": end-of-line

# for freebsd console
# "\e[H": beginning-of-line
# "\e[F": end-of-line

#$endif

Should read more 'bout that modes. Thanks everybody for the trouble-taking!

I've had the same problem. My /etc/inputrc was configured correctly, but due to some strange reason I had skeleton configuration in ~/.inputrc which then disabled all the mappings in /etc/inputrc.

So, my solution was:

rm ~/.inputrc