SimpleDateFormat parsing date with 'Z' literal

The date you are parsing is in ISO 8601 format.

In Java 7 the pattern to read and apply the timezone suffix should read yyyy-MM-dd'T'HH:mm:ssX

tl;dr

Instant.parse ( "2010-04-05T17:16:00Z" )

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ISO 8601 Standard

Your String complies with the ISO 8601 standard (of which the mentioned RFC 3339 is a profile).

Avoid java.util.Date

The java.util.Date and .Calendar classes bundled with Java are notoriously troublesome. Avoid them.

Instead use either the Joda-Time library or the new java.time package in Java 8. Both use ISO 8601 as their defaults for parsing and generating string representations of date-time values.

java.time

The java.time framework built into Java 8 and later supplants the troublesome old java.util.Date/.Calendar classes. The new classes are inspired by the highly successful Joda-Time framework, intended as its successor, similar in concept but re-architected. Defined by JSR 310. Extended by the ThreeTen-Extra project. See the Tutorial.

The Instant class in java.time represents a moment on the timeline in UTC time zone.

The Z at the end of your input string means Zulu which stands for UTC. Such a string can be directly parsed by the Instant class, with no need to specify a formatter.

String input = "2010-04-05T17:16:00Z";
Instant instant = Instant.parse ( input );

Dump to console.

System.out.println ( "instant: " + instant );

instant: 2010-04-05T17:16:00Z

From there you can apply a time zone (ZoneId) to adjust this Instant into a ZonedDateTime. Search Stack Overflow for discussion and examples.

If you must use a java.util.Date object, you can convert by calling the new conversion methods added to the old classes such as the static method java.util.Date.from( Instant ).

java.util.Date date = java.util.Date.from( instant );

Joda-Time

Example in Joda-Time 2.5.

DateTimeZone timeZone = DateTimeZone.forID( "Europe/Paris" ):
DateTime dateTime = new DateTime( "2010-04-05T17:16:00Z", timeZone );

Convert to UTC.

DateTime dateTimeUtc = dateTime.withZone( DateTimeZone.UTC );

Convert to a java.util.Date if necessary.

java.util.Date date = dateTime.toDate();

Java doesn't parse ISO dates correctly.

Similar to McKenzie's answer.

Just fix the Z before parsing.

Code

String string = "2013-03-05T18:05:05.000Z";
String defaultTimezone = TimeZone.getDefault().getID();
Date date = (new SimpleDateFormat("yyyy-MM-dd'T'HH:mm:ss.SSSZ")).parse(string.replaceAll("Z$", "+0000"));

System.out.println("string: " + string);
System.out.println("defaultTimezone: " + defaultTimezone);
System.out.println("date: " + (new SimpleDateFormat("yyyy-MM-dd'T'HH:mm:ss.SSSZ")).format(date));

Result

string: 2013-03-05T18:05:05.000Z
defaultTimezone: America/New_York
date: 2013-03-05T13:05:05.000-0500