The norm is joint tenancy with rights of survivorship, for married couples.
In general there's three types of tenancy: common, joint, and by the entirety. Nebraska doesn't recognize by the entirety so that's out.
Nebraska assumes that unless stated as joint, the property owned by more than one person, even husband and wife, is tenancy in common.
Joint tenancy gives each party an undivided interest such that when one of you dies, the other gets ownership to the property (in some states other than Nebraska, you must explicitly state the survivorship interest, and it's not uncommon in Nebraska, but not strictly necessary). The only minor downside is that you can't divest your interest jointly held property alone. However, a joint tenant has the option (without the permission of the other property) to convert the joint tenancy to tenancy in common.
Tenancy in common says you own half and your wife owns half (or whatever share is stated in the deed). You're free to sell your share if anybody would be interested in buying it. When you die, your will or the laws of intestate succession determine how ownership of your share would be distributed. If you have no will and you have either children (or their descendants) or surviving parents, the spouse splits your share with those people.