System.currentTimeMillis() vs. new Date() vs. Calendar.getInstance().getTime()

System.currentTimeMillis() is obviously the most efficient since it does not even create an object, but new Date() is really just a thin wrapper about a long, so it is not far behind. Calendar, on the other hand, is relatively slow and very complex, since it has to deal with the considerably complexity and all the oddities that are inherent to dates and times (leap years, daylight savings, timezones, etc.).

It's generally a good idea to deal only with long timestamps or Date objects within your application, and only use Calendar when you actually need to perform date/time calculations, or to format dates for displaying them to the user. If you have to do a lot of this, using Joda Time is probably a good idea, for the cleaner interface and better performance.

Looking at the JDK, innermost constructor for Calendar.getInstance() has this:

public GregorianCalendar(TimeZone zone, Locale aLocale) {
    super(zone, aLocale);
    gdate = (BaseCalendar.Date) gcal.newCalendarDate(zone);
    setTimeInMillis(System.currentTimeMillis());
}

so it already automatically does what you suggest. Date's default constructor holds this:

public Date() {
    this(System.currentTimeMillis());
}

So there really isn't need to get system time specifically unless you want to do some math with it before creating your Calendar/Date object with it. Also I do have to recommend joda-time to use as replacement for Java's own calendar/date classes if your purpose is to work with date calculations a lot.

If you're USING a date then I strongly advise that you use jodatime, http://joda-time.sourceforge.net/. Using System.currentTimeMillis() for fields that are dates sounds like a very bad idea because you'll end up with a lot of useless code.

Both date and calendar are seriously borked, and Calendar is definitely the worst performer of them all.

I'd advise you to use System.currentTimeMillis() when you are actually operating with milliseconds, for instance like this

 long start = System.currentTimeMillis();
    .... do something ...
 long elapsed = System.currentTimeMillis() -start;