In the beginning, there were 95-characters and a url. Plain and simple, just some text relevant to what you have just queried.
As the AdWords platform has evolved so have the ways and means with which to embellish these 4 lines of text, providing either a richer or poorer searching experience, depending on your personal preference. These extra features of adverts are known as 'Ad Extensions' within the programme.
This blog hopefully serves as an introduction to the extra information and elements you can use to enhance your adverts and gives an idea of the benefits they can provide.
Getting started with Ad Extensions
If you haven't used them before, then the tab will need to be enabled. Just click on the small drop-down icon at the end of your existing tabs, and you'll be able to check the box to start showing:

Once the previously hidden tab has appeared you'll be presented with an ever-growing number of options to choose from.

Lets have a look at the current options available to advertisers:
Location Extensions
Locality play a huge part in how relevant your business offering is to a potential customer. This extension allows an address to be pulled in from your places page or entered manually.

By showing this address you can expect greater click-through rates from qualified customers, and potentially stop wasted clicks – if location is a relevancy factor for customers then you don't want budget spent bringing users to the site, only for them to find out it isn't relevant to them.
It's worth noting that these can also be shown with reveal/hide map:

Call Extensions
Allows users to bypass the website and get in touch direct with a business over the phone.

Sitelinks Extensions
If memory serves me, this was the first extension available, and is now probably the most commonly used. Sitelinks essentially allow you to replicate how brand organic listings look, with sub-links below the main copy:

This is really useful as you can provide even more targeted landing pages, whilst getting more real estate on the SERPs.
In the above example, a generic search for 'hotel glasgow' allows the ad to appear highly relevant to users who already are focused on a particular area. Landing them directly on these pages can help improve conversion rates by taking out unnecessary navigation once through to the site.
Product Extensions
By connecting your Google Merchant Center account to AdWords, relevant product details will be pulled in, giving you some of the first adverts with images on the Google SERPs:

These can be great for helping improve ROI for retail PPC campaigns. At a basic level products are chosen automatically by Google, but with a bit of tweaking to your product feed there can be a level of control over which products are shown (more on how to do this here).
Social Extensions
Enhance the clout of your advert by linking a Google+ page to your adverts. Social proof is a powerful weapon, so the click-through rate will get a boost by having this extra layer of credentials added on:

Seller Rating Extensions
Only available at the behest of Google, these automatically start appearing if there are enough high ratings (4 out of 5 at least) for your domain on sites aggregated by Google or from Google Checkout users.

Beneficial for improving click-through rates and conversion rates (as a result of making a cracking first impression).
You can find out what views and reviews Google can see for your site by sticking your domain on the end of this here url:
http://www.google.co.uk/products/seller?zmi=
Making sure you have reviews visible to Google is a strategy in itself but is well worth the time and effort.
Mobile App Extensions
One of the NKOTB, this extension adds a direct link to either iTunes App Store or Google Play (the artist formerly know as the Android Marketplace):

Closing thoughts
Across the board, all of these extensions are great for improving your PPC campaign's click-through rates, but each also have individual assets. It's worth taking some time to implement them and understand how and when they can have the best impact.