What antivirus software do you use? There is a chance that you do actually have a large number of trojans, but your antivirus software could be "rogue." Symantec Norton, McAfee, TrendMicro, BitDefender, Panda, CA, Sophos, Norman, ESET, Avira, avast!, ZoneAlarm, and AVG are trusted brands. However, "rogue" antivirus software will tell you that you have a large number of viruses, when really it is just a virus itself. Although the FTC shut down WinFixer, a vendor of rouge antivirus softwares which included ErrorSafe, DriveCleaner, XPAntivirus, AV System Care, FreePCSecure, and VirusDoctor, there is still a wide range of rogue softwares out there.
To see if your computer does have a large number of trojans, I would use either of these two free scanners, which will disinfect threats. However, for free antivirus software that works proactively 24/7, I would recommend avast! Antivirus at http://www.avast.com/.