Seriously, if you're spending more than a few minutes a week SSH'ing then forget PuTTY, grab yourself a copy of MobaXterm:

http://mobaxterm.mobatek.net/

It's also Pageant aware and will use that as your ssh key agent if you prefer. And vim works properly. We like it so much we pay for the Pro editions.

"Max. 12 sessions Max. 2 SSH tunnels Max. 4 macros Max. 360 seconds for Tftp, Nfs and Cron"

Not open source and heavily limited. Unless you pay for Pro, it's pretty useless...

If you just have a handful of servers you can still get a lot done with the free edition, not useless at all by any stretch of the imagination. Paying a few quid a year to keep up with the updates is peanuts compared to the extra productivity we get from it.

Sounds like VT emulation settings in PuTTY might be wrong. There's nothing in vim that PuTTY doesn't support - in fact I've used vim over PuTTY many times.