Implement equals(). Make sure you comply with the contract of the method.
Also, if you search often and the array is large you probably want to consider a better data structure for this, e.g. one of the implementations of Set if you're interested in the presence of particular instances within the data structure or one of the implementations of Map if you want to search by a key. See java.util for details.
Note that some of the data structures in java.util may require you to provide your own version of hashCode() (e.g. HashSet) and some may require you to implement Comparable interface or provide a Comparator (e.g. TreeSet).
If you provide your own version of hashCode() make sure it is consistent with your equals() (see the javadoc for equals()).
If you really must use an array, then consider one of the versions of Arrays.binarySearch(). Note that you can only use it on sorted arrays.