You are the legal owner of the house, even though she is on the mortgage. However, she may have some spousal rights to some of the value in the house in the event of a divorce. You should retain domestic counsel to assist you in this.
If only your name appears on the deed, then you are the sole owner of the home from a legal standpoint. However, your wife may have an equity interest in the home. In general, any property acquired during the marriage is considered marital property subject to equitable division, unless acquired via gift, inheritance, of excluded by agreement. If you purchased the home prior to the marriage, it initially was non-marital property. However, since the marriage, if marital funds were used to acquire equity in the home (mortgage payments), then a portion of the equity would be considered marital property.