There's been lots of people reporting that Contact Form 7 stopped working in WP 3.4 - exactly the same for me with a number of sites.
The behaviours I've been experiencing is the form saying it's successful but then no messages coming through - started happening on about 9 different sites (I've stopped from upgrading WP on all others just now) - but then no messages ever got emailed through.
I just ran a search on my gmail account and have found dozens of contact form messages in my spam folder!
I've therefore recovered them and created a rule that will hopefully stop all future messages from being binned.
Not sure if there's something in WP3.4 or Contact Form 7 plugin that has suddenly made contact form messages appear as dodgy spam mails?
Hope this helps others who've been scratching their heads.