What should I use instead of the deprecated Date.getHours()

As others already stated Javadoc suggests to instead use Calendar.get(Calendar.HOUR_OF_DAY).

Deprecated. As of JDK version 1.1, replaced by Calendar.get(Calendar.HOUR_OF_DAY).

Here's how you could do it for already set Date:

int getHourOfDay(Date date) {
    Calendar calendar = Calendar.getInstance();
    calendar.setTime(date);
    return calendar.get(Calendar.HOUR_OF_DAY);
}

Use Calendar.HOUR_OF_DAY if you want number from 0-23 and Calendar.HOUR for 0-11.

Javadoc explicitly suggests

Deprecated. As of JDK version 1.1, replaced by Calendar.get(Calendar.HOUR_OF_DAY).

Joda library is another best alternative to handle Date and Time.

These methods are indeed deprecated.

You should now use java.util.Calendar#get()

So your example becomes

Calendar cal = Calendar.getInstance();
cal.get(Calendar.HOUR);

see the javadoc of this class.

Note that you can get a Date object by calling getTime on cal.