I looked into this a while back, when HSBC started whining about it. Ostensibly, I wanted to know what it actually did.
When I looked at it, Trusteer’s website was a typical marketing-focused site. It tells you all about how Rapport ‘secures transactions’ and prevents malware, but didn’t have one jot of information about how it actually does that. For that reason, I decided that it wasn’t for me; I don’t want some unknown software doing secret, mysterious things that might well conflict with other systems I use.
Looking at it now though, it seems they’ve improved it somewhat.
http://www.trusteer.com/Products/Trusteer-Rapport-for-Online-Banking
From this, it looks like it sandboxes the browser and checks for keyloggers and such. I’m not immediately seeing much benefit over other conventional tools though. Where it sounds like it might win is prevention against user naivety; for people who don’t know any better than to click links in scam spam emails, it might well be a really good idea. So whilst I’m not as wholly suspicious as I was about it, I don’t think I’m they’re target audience.