I cant trust my boyfriend, so should I stay with my him?

Well my partner and i have been together for jut over two years now, i love him dearly, but the main problem is trust.
He seems to think it is ok to lie about things, because it will either avoid an argument or get me to listen to him......But the lying is what causes the arguments and why would you lie to someone to get them to listen? I dont want to listen anymore because he does lie.
The other main problem is his hiding things....he is constantly on the computer and he always clicks off the screen if i come in the room, but he always denies this.
The other day he did admit that he hid a photos folder from me on the computer because he didnt know what pictures were in there.
I dont understand why he had to hide them. He could have been honest and said "i havent been in this folder for a while, so there may be some old photos from exes before we got together" and that would have been fine, everyone has forgotten pictures or gifts from exes.
He always has a way to justify lying or hiding things, but if i did any of those things, he would think that i am the most terrible girlfriend.
I think the most important thing in a relationship is trust, but its the one thing we dont have. So i guess my question is: Even though i love my boyfriend, should i stay with him if i cant trust him?