How to use enum values in f:selectItem(s)

JSF has a builtin converter for enum, so this should do:

@ManagedBean
@ApplicationScoped
public class Data {

    public Status[] getStatuses() {
        return Status.values();
    }

}

with

<h:selectOneMenu value="#{bean.question.status}" >
    <f:selectItems value="#{data.statuses}" />
</h:selectOneMenu>

(note: since JSF 2.0 there's no need anymore to provide a SelectItem[] or List<SelectItem>, a T[] and List<T> are accepted as well and you can access the current item by var attribute)

If you happen to use JSF utility library OmniFaces, then you could use <o:importConstants> instead of a bean.

<o:importConstants type="com.example.Status" />

<h:selectOneMenu value="#{bean.question.status}" >
    <f:selectItems value="#{Status}" />
</h:selectOneMenu>

If you intend to control the labels as well, you could add them to the Status enum:

public enum Status {

    SUBMITTED("Submitted"),
    REJECTED("Rejected"),
    APPROVED("Approved");

    private String label;

    private Status(String label) {
        this.label = label;
    }

    public String getLabel() {
        return label;
    }

}

with

<f:selectItems value="#{data.statuses}" var="status"
    itemValue="#{status}" itemLabel="#{status.label}" />

Or, better, make the enum value a property key of a localized resource bundle (EL 3.0 required):

<f:selectItems value="#{data.statuses}" var="status"
    itemValue="#{status}" itemLabel="#{text['data.status.' += status]}" />

with this in a properties file associated with resource bundle #{text}

data.status.SUBMITTED = Submitted
data.status.REJECTED = Rejected
data.status.APPROVED = Approved

For localization we can use also this solution:

public enum Status { SUBMITTED, REJECTED, APPROVED }

data.status.SUBMITTED=Submitted
data.status.REJECTED=Rejected
data.status.APPROVED=Approved

<h:selectOneMenu value="#{bean.question.status}" >
    <f:selectItems
        value="#{data.statuses}"
        var="status"
        itemValue="#{status}"
        itemLabel="#{text['data.status.'.concat(status)]}" />
</h:selectOneMenu>

So the resource path for localization strings are not hardcoded in Enum.

You could use <f:selectItems value="#{carBean.carList}" /> and return a list of SelectItem instances that wrap the enum (use Status.values() to get all possible values).