How to fix Ctrl + arrows in Vim?

Figure out exactly what escape sequence your terminal sends for Ctrl+arrow by typing Ctrl+V, Ctrl+arrow in insert mode: this will insert the leading ESC character (shown as ^[ in vim) literally, followed by the rest of the escape sequence. Then tell vim about these escape sequences with something like

map <ESC>[5D <C-Left>
map <ESC>[5C <C-Right>
map! <ESC>[5D <C-Left>
map! <ESC>[5C <C-Right>

I seem to recall that Putty has a default setting for Application Cursor Keys mode that's inconvenient (I forget why), you might want to toggle this setting first.

Note that although escape sequences vary between terminals, conflicts (i.e. an escape sequence that corresponds to different keys in different terminals) are rare, so there's no particular need to try to apply the mappings only on a particular terminal type.

Your best bet is probably to look at PuTTY's Application Cursor Keys mode configuration.

The default sequences send ESC as a prefix and [ followed by Append or Change or other things throwing you into insert mode.

added, following Gilles

A slightly more explicit version of the ^V escape can be seen with od(1). Here is me typing ^Up, ^Down, ^Right, ^Left at my terminal:

$ od -a
0000000 esc   [   1   ;   5   A esc   [   1   ;   5   B esc   [   1   ;
0000020   5   C esc   [   1   ;   5   D

So my terminal sends ^[[1;5A when I press Ctrl + ↑

I found a better solution here: http://vim.wikia.com/wiki/Fix_arrow_keys_that_display_A_B_C_D_on_remote_shell

Just put this string in your .vimrc file:

:set term=cons25

Update

Copy this file to your /home, renaming it .vimrc:

/usr/share/vim/vim_VERSION_/vimrc_example.vim