For divorce: Please note, there are more grounds available than those listed here (adultery, alcoholism / addiction, imprisonment, psychiatric commitment, deviant sexual conduct). The below are the most commonly used, especially in an uncontested case.
If you and your spouse have been separated for a period in excess of 18 months and there is no reasonable prospect of reconciliation, you are eligible to use no fault instead of asserting "fault-based" grounds.
18 months separation
Extreme Cruelty (What is "extreme cruelty lite"?)
Irreconcilable Differences (6 months or more)
Your spouse must have left over a year ago and against your wishes to be eligible for a divorce on the grounds of desertion. Can also be used if the parties reside under the same roof but the defendant has willfully refused to engage in sexual relations for a period in excess of one year.
Annulment: The difference between annulment and divorce is that if a marriage is annulled, it "never existed" - if the marriage being annulled was you first marriage, then your next marriage will be your "first." Again, there are other grounds for annulment available, but the most common is an allegation that there was "fraud at the base" of the marriage. Usually, this is satisfied by an allegation that the other party did not have the intent to enter into a marriage, and that you would not have entered into the purported marriage had you been aware of this (Example: "Three months after the wedding, defendant informed me that I was only married to make an ex jealous".) A legal annulment is not the same thing as a religious annulment, which can only be granted through a church. If you plan to seek a religious annulment, consult an attorney who is familiar with the process. What you allege in a legal annulment or divorce complaint can have an effect on whether the church subsequently annuls the marriage. The Court will generally have little problem with an annulment if the marriage was brief (less than a year) and there are no children.