Is it possible to monitor Wi-Fi usage in a similar method to how 3g watchdog monitors 3G usage? I have android 2.2 on my phone. I doesn't need to do everything 3G watchdog does, all I need to see is how much data I am using.
Netcounter can monitor both cellular data and wifi usage levels.
My Data Manager also does a great job.
Tracks wifi and cellular down to the app level. You can have it warn you when you are near a data cap. You can set it up to track by calendar month or by your billing cycle.
It has a widget as well as a notification bar item.
I used it to track down my runaway data usage (Doggcatcher) on my phone as well as a build.prop error causing huge data usage on my son's MIUI Incredible.
Take a look at DU Meter for Android. DU Meter can show current network transfer rates in the notification area, it includes a home screen widget which displays daily or monthly data usage, etc.
Disclaimer: I'm the author of DU Meter.
For more options, you can also try Traffic Monitor; it monitors both cellular and wifi usage as well. And you can also check usage per app.