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.
As of the February 2017, there are a few chime Devices available that work with SmartThings, including one that allows you to upload your own sound files. There are several different ways to make this work depending on what you were trying to accomplish.
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.
Alternatively, maybe you don't want a chime when the door opens, but you want a chime in a different part of the house when the doorbell button is pushed on the outside of the house. In that case, you can either use the Aeon doorbell which comes with its own button or you can get the Nexia doorbell sensor which is wired into your existing nonnetworked chime and will inform your SmartThings hub when that chime sound. Or you can use any of the fancy video doorbells like Ring which have a SmartThings integration. Then you use that "doorbell pressed" event as the trigger to have other chimes sound elsewhere in the house. And again, you can use SmartThings to add additional conditionals like mode or time of day.
Getting a Spoken or Sound Effects Alert from Amazon Echo When a Sensor is Triggered
You will do this with an Amazon echo routine (not a SmartThings routine). It's very simple to set up. Official Alexa Instructions. You can have the same Amazon echo routine turn on lights.
For many people who already have Amazon echo devices, this may be all you need, as long as you're OK with a chime/announcement which depends on the Internet working.
Devices to Make a Chime Sound Once SmartThings Recognizes the Trigger Event
'1. The Aeon Doorbell ($69)
One very straightforward solution is to get the $69 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.
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.
Note that you need to get the "doorbell" model, not the "siren" model so you can upload your own sounds.
UK Note: this device was originally manufactured on both the US and the UK frequencies, but since it was first released, the UK version has become very difficult to find. So you may not be able to use this option in the UK.
Community discussion thread with the device type handler code: ]
Amazon listing 
2. Dome Chime ($35) US Only)
3. UEI / Xfinity Keypad Model XHK1 with Tone ($10-$20) (US Only)
UEI makes a Zigbee security keypad which has a built in tone. There is only one tone sound, it also has a motion sensor and temperature sensor build into it. It runs on 4 AA batteries (Lithium, Alkaline or rechargeable NiMH/NiCd). Same device is also sold for the Xfinity home system.
eBay listing 
4. Lowes Iris Keypad Model 3405-L with Tone ($49) (US Only)
Lowes makes a zigbee security keypad which has a built in tone. There is only one tone sound. Earlier models were not compatible with SmartThings, so check the model number. Same device is also sold for the Xfinity home system.
There are several different custom device type handlers available for it, each with slightly different features. These are available on the quick browse list in the device Type handler section on the security list.
Lowe's listing 
5. Ring Doorbell with Optional Chime Unit (US AND UK)
Official support article: https://support.smartthings.com/hc/en-us/articles/214288206-Ring-Doorbell
6. Power Failure Alert plus SmartThings power outlet (total $35-$55) (Both US and U.K. Choices, but with different brands)
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.
7. Alarm Clock Alert (Price is the cost of the clock, plus $20 for the outlet)
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.)
8. Various Text to Speech(TTS)/Custom Sound Speakers (cost varies, but is typically $150 and up)
As of November 2016, the echo does not have a specific text to speech feature, although the company has indicated that may be coming in 2017. So you will have to use other methods for that for now. You can use the quick browse lists in this wiki and look under either alerts or voice to find those options. 
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.
9. 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.
For more information
For help setting up a specific notification, ask in the community forum