Unfortunately most people who accuse their spouse of cheating when there is no basis behind it are suffering from insecurities themselves. Maybe try to affirm your love and faithfulness with him by reminding him often of your attraction to him and your lives together. And as drac said, if your life is transparent to him that leaves little to no room for errors that may look suspicious to someone who is feeling paranoid and insecure.
Be aware though, that although it doesnt always sometimes intense insecurities on your partners part may cause them to begin to try to control your actions so that they may always 'know what you are up to'
If you have not cheated on him and have given him no reason to suspect that you have, then there is something wrong with him. Some people who are abnormally jealous or paranoid try to control their partners.
If he is so insecure he probably needs professional help to overcome it. But don't let his suspicions make you tip toe around him.
Thank you all for your replies. The suspicions have been getting worse over the years. I guess my life is kinda transparent because I go to work, come home, go to PTA meetings, etc. pretty boring. He says the reason for the mistrust is because early into our relationship I held back my feelings in general (my way of keeping up my guard, whether it was right or wrong, I did it) and now I feel as though I am being punished for that. I have told him if he felt that way and didnt trust me then why marry me?? The answer.....I hoped you would open up. I don't know how much more open I can now be...I talk about my day, his day, us, everything. Once he accussed me of not being at the bank when I said I was because my two deposit slips said two different times. We fought for a whole day or so about this. Until he went to the bank and found out that there computer system was screwed up and it wasn't me. And all I got was "sorry". I asked him why he didn't put as much effort into his apology as he did his accusations? I got "but I said I was sorry". I don't know what to do. Sometimes it feels like too much time and aggravation to keep trying but then I remember and still see the great times together. I don't know, but I know I need to be happy somehow whether it's together or separate....??