Cold sores are caused by herpes simplex virus 1, or hsv1. Many, many people have this. About half the adult population has it. Most will get it in childhood, from a relative kissing them, usually, and 90% will never get a cold sore, so they don't know they have it.
When he does have a cold sore, you should definitely avoid kissing him. He can kiss your cheek, but shouldn't kiss your lips. The skin on your cheek is thick enough that you won't get infected that way, but the skin on your lips is thinner.
I don't know how sexually active you've become, or plan to become, and you don't have to tell me, but you should also know that if he gives you oral sex, you could get genital herpes type 1 from him. This is quite common, and about half of all new genital herpes infections are the result of oral sex.
He can transmit it without a sore, too, because of something called asymptomatic viral shedding. This is where the virus is active on the skin but he has no symptoms. With oral hsv1, this happens about 25% of days per year.
If he is getting a lot of cold sores, he should talk to his doctor about taking a medication like valtrex every day. This will help prevent the cold sores, and also reduce the shedding, and reduce transmission.
This may all sound scary, but in some ways, you are safer with someone who knows they have this. He knows what a cold sore feels like when it's coming, and can avoid kissing you then. Someone who doesn't know they have it doesn't know when to avoid kissing or more.
If you like him, this shouldn't be a reason to leave him, since the next guy you date has a really good chance of having it, too. I always say that herpes (either oral or genital) isn't a good reason to leave a great relationship, or a good reason to stay in a bad relationship.
It's up to you, of course. :)
Let us know if you have any questions.