How to handle TimeZone properly in SQL Server?
There's no quick fix for this, unfortunately. Internationalization of an application should be part of the very first design discussions, as it really goes to the core of a lot of different areas, including date/time comparisons and output formatting.
Anyways, to get on the track of Doing It Right, it's essential to store the time zone information with the time. In other words, realizing that the date/time 20130407 14:50 is meaningless without either (a) including the time zone's then-current UTC offset(note 1), or (b) ensuring that all logic inserting these values first converts to a certain fixed offset (most likely 0). Without either of those things, two given time values are incomparable, and the data is corrupt. (The latter method is playing with fire(note 2), by the way; don't do that.)
In SQL Server 2008+, you can store the offset with the time directly by using the datetimeoffset data type. (For completeness, in 2005 and before, I would add a second column to store the then-current UTC offset value (in minutes).)
This makes it easy for a desktop-type application, as these platforms normally have mechanisms to automatically convert a date/time + time zone to a local time and then format for output, all based on the user's regional settings.
For the web, which is an inherently disconnected architecture, even with the back-end data set up properly, it's more complex because you need information about the client to be able to do the conversion and/or formatting. This is usually done via user preference settings (the application converts/formats things before output), or simply showing things with the same fixed format and time zone offset for everyone (which is what the Stack Exchange platform currently does).
You can see how if the back-end data is not set up properly, very quickly it's going to get complicated and hacky. I would not recommend going down any of those paths because you'll just end up with more problems down the line.
Note 1:
A timezone's UTC offset is not fixed: consider daylight savings where a zone's UTC offset varies by plus or minus an hour. Also zones' daylight savings dates vary on a regular basis. So using datetimeoffset (or a composite of local time and UTC offset at that time) results in maximum information recovery.
Note 2:
It's about controlling data inputs. While there's no fool-proof way to validate incoming values, it's better to enforce a simple standard that doesn't involve computations. If a public API expects a data type that includes an offset, that requirement will be clear to the caller.
If that wasn't the case, the caller has to rely on documentation (if they read it), or the computation is done incorrectly, etc. There are fewer failure/bug modes when requiring an offset, in particular for a distributed system (or even just web/database on separate servers as the case here).
Storing the offset anyway kills two birds with one stone; and even if that isn't required now, it makes the possibility available later on if necessary. True it takes up more storage, but I think it's worth the trade-off because the data is lost if it's never recorded in the first place.
I have developed a comprehensive solution for time zone conversion in SQL Server. See SQL Server Time Zone Support on GitHub.
It properly handles conversions between time zones, and to and from UTC, including daylight saving time.
It is similar in concept to the "T-SQL Toolbox" solution described in adss's answer, but it uses the more common IANA / Olson / TZDB time zones instead of Microsoft's, and it includes utilities to keep the data maintained as new releases of the TZDB come out.
Example usage (to answer the OP):
SELECT Tzdb.UtcToLocal(sysutcdatetime(), 'Asia/Riyadh') as CurrentTimeInSaudiArabia
See the readme on GitHub for additional APIs and detailed explanation.
Also, note that since this is a UDF based solution, it is not designed with performance as the primary objective. It would still be better if this functionality was built in to SQL Server, similarly to how the CONVERT_TZ function exists in Oracle and MySQL.
SQL Server made modifications in 2005 onward where the internal timezone is saved in UTC. This was largely due to geo-replication and HA projectors involving log shipping, and having the log shipping times saved in different time zones made it impossible for the old method to restore them.
Thus, saving everything internally in UTC time allowed SQL Server to work well globally. This is one of the reasons why daylight savings is kind of a pain to deal with in Windows, because other MS products such as Outlook also save the date/time internally as UTC and create a offset that needs to be patched.
I work in a company where we have thousands of servers (not MS SQL Servers though, but all kinds of servers) spread out all across the world, and if we didn't specifically force everything to go by UTC, we would all go insane very quickly.