How to Set Up a Door Open Chime/Siren
There are several reasons why someone why someone would want an audible alert in the house when a door is opened, rather than just a text or push notification.
For example, if you have a child who wanders, you might want the adults to wake up if a particular door is opened at night.
Or you might want the equivalent of a doorbell if a front gate is opened.
There are many different contact sensors available for use with SmartThings which can detect the door being opened. That part is easy. The question is how do you set up a device to make an audible alert when the sensor send the "door opened" message to the hub?
As of the summer of 2016, there is no simple chime device available that works with SmartThings. However, there are many different ways to make this work depending on what you were trying to accomplish.
All of these options will require that you also have a contact sensor on the door that you are monitoring, or some other device to notify SmartThings of activity. You will need one sensor per door. These generally cost around $20 each although they can sometimes be found on sale as low as $15.
Once you have set up the basic alert (door opens, sound plays) if desired, conditionals such as time of day, mode, etc. can be added through the usual SmartThings logic.
1. The Aeon Doorbell ($49)
One very straightforward solution is to get the $49 Aeon doorbell. This has two parts: a Z wave speaker and a wireless button remote for the speaker. You can use the button as a panic button or a doorbell button.
For the purposes of this how to, though, we are only interested in the speaker unit. This device can play up to 99 different custom sound files, so you can make anything you like from a Windsor bell to a spoken notification. It also comes with some built-in sounds including a chime. You can trigger the speaker with a SmartThings command, which means you can play different tracks for different SmartThings events, including a door sensor recognizing that the door is open.
So the solution is fully integrated with SmartThings, gives you many different sound options, and you can use any trigger event that SmartThings can recognize.
There are two negatives. First, the device can be quite fussy to get paired initially, with some people reporting that they have to try 15 or 20 times. (This pairing difficulty is the main reason for the low Amazon ratings.) Secondly, the device will require custom code. There are two different community-created Device type handlers, both approved by the doorbell manufacturer, which work very well and offer slightly different features. And people in the community will be glad to help you get things set up. But it's not quite as simple as just using the official "add a new device" feature.
Still, once you get this device set up the way you want it, it will solve most of the use cases that people have. You can also use different sounds for different doors.
Note that you need to get the "doorbell" model, not the "siren" model so you can upload your own sounds.
Community discussion thread with the device type handler code: 
Amazon listing 
2. Power Failure Alert plus SmartThings power outlet (total $35-$55)
If you want a more annoying sound, perhaps to discourage a family member from opening the door, or you want a solution with A very easy set up, you can purchase a "power failure alarm," plug it into any networked power source that works with SmartThings, and use the official "smart lighting" feature to turn the power source 'off' when the contact sensor reports "door open." That way when the door is opened, SmartThings will turn off the power to the alarm, the alarm detects the power loss and sounds its beeper.
The beepers are typically loud and annoying. People use them without a home automation system for freezers or even medical equipment that lose power. They cost anywhere from $15-$35 at Amazon or any home-improvement store. You also need to purchase a networked power supply device that SmartThings can control, typically a pocket socket for about $20.
Most people won't want these for a doorbell, but they can be useful as a deterrent for family wanderers.
You also will have several options for how to turn the beeper off again. Just turning on the networked power source will do it. Some people will have things set up so just the door closing again will turn off the beeper, but that's not usually what you want for a wanderer alert. Instead, you may want to just use the official phone app and toggle the switch, or put a button on the wall. But again, to SmartThings this is just an outlet that's being turned on and off, so you will have a lot of choices.
At $15, the reliance controls plug in power failure alert is a good choice for a beeper device when you want a "door open" alarm which is not as overwhelming as a typical security siren, but is still annoying enough to be a deterrent. . There are many similar brands as well. You also need to purchase a SmartThings – controllable power outlet, typically around $20. So this specific setup should cost a little less than the Aeon Doorbell, but only has one sound option.
3. Alarm Clock Alert (Price is the cost of the clock, plus $20 for the outlet)
Before the Aeon doorbell was available, some people would use the same set up as the power outage beeper, but would instead plug in an alarm clock of the kind where once the alarm sounds, it continues to sound until you press the button, and if you unplug it in the middle of sounding and then plug it back in again it continues to sound once the power comes back on. So for this set up you just have SmartThings turn on the power to start the alarm clock sounding and turn off again to stop the sound.
This generally gives you a choice of sounds which are less annoying than the power failure beepers. Some are even suitable as doorbells. The trick is to find one that will go right back to sounding when power is restored. Some models will, some won't, so you may just have to try a few. (If the clock has a battery backup feature, do you not use it – – just take out the battery. You want the clock to be off when the power is off and on when the power is on.)
For this method you still have to buy all three devices: contact sensor for the door, alarm clock for the sound, and networked power source so that there is something for SmartThings to control. Set up is easy, and you can just use the official smart lighting feature. If you already have a alarm clock you can repurpose, then the cost will be lower than the Aeon Doorbell. But this solution will be limited to only one sound option.
4. Various Text to Speech(TTS)/Custom Sound Speakers (cost varies, but is typically $150 and up)
Some speakers such as Sonos have the ability to play custom sound files, from dogs barking to spoken announcements, and these can be used. An Amazon echo can also be used as a Bluetooth speaker in a similar fashion. Each device model requires a specific smartapp, so if you are interested in this approach the best thing is just to search the forums for that specific device and "notifications." For example there is one for Sonos, a completely different one for Amazon echo, etc.
All of the devices in this category cost more than the simple alert devices or the Aeon doorbell discussed above so in most cases you would only choose this method if you already had the speaker device for other reasons.
5. Android as an Audible Alert (requires an android phone/tablet)
The LANNouncer app for android (formerly called Landroid) requires an android device. Set up is fairly complicated, but this gives you a lot of different function options. Essentially lets you use an android device in the same way that the TTS speakers work. Community discussion thread with links to the software 
Smoke Detectors, including the Nest Protect, Cannot be Used for Custom Alerts
Residential Smoke detectors sold in the US have to meet a number of specific safety requirements. One of these is that the smoke detector announcement system cannot be used for custom alerts. The concern is that you might miss a fire alert because the speaker was busy telling you the laundry had just finished. So these devices cannot usually be Repurposed as door open alerts.
There are some home security systems which are classified as multipurpose alerts rather than smoke detectors, that do have the ability to Play custom spoken alerts for intruder detection, which would include a door being opened. For these, you need to check the details of each individual system to see what is available.