I have Norton AntiVirus, but still regularly get Trojans?

Those trojans are most probably spyware. I've yet to see an antivirus program that is very good in detecting spyware. That's why we need dedicated antispyware programs like MBAM or SUPERAntiSpyware to detect them. However, if you are only using the free version of MBAM or SAS then you can't stop spyware from entering your computer. Those free versions are only on-demand scanners. If you want real-time protection, get the pro version. A lifetime license for MBAM Pro only costs $24.95 if I'm not mistaken.