I think it's best to be as honest as you can be in a relationship- especially about serious topics- but you don't have to tell each other everything. There are certain things I would never tell another person, simply because they're personal and not relevant to anyone but myself. And a little white lie here and there is sometimes kinder than the truth. However as I said, if you're keeping a secret about something serious that's a different matter, because you should be able to share it with your partner.
Some secrets are meant to be shared. However, one needs to weigh the seriousness of the secret. Some infractions in a marriage, for instance, should not be revealed if they will hurt the other person too much. That is something that needs sensitivity, even though it's usually better not to keep secrets.
The major backbone to any relationship is trust. Without trust a relationship will crumble and cease to exist. I do not believe it is a good idea to keep secrets in relationships and I do believe secrets can hurt relationships in the long run. Relationships are about experiencing life in all aspects.