1. Shorten links in presentation slides because...
Most normal-length web addresses are quite fiddly to write down at speed. If your talk includes a link to a website or an online document please make it easy for your audience to make a note of it within the minute and a half you have your slide visible on-screen.
Eg... the one with the green tick is easier to scribble down than the one with the red cross next to it.
If your presentation has lots of links then first create a page on your website or blog (if you don't have one there are other free suggestions below). Add all your links there, then shorten the address of that page and put that shortened link in your presentation. Your audience cannot help but be kindly disposed to you :)
You can also have that shortened link running over several slides making it easier for your audience (in fact why not say "this link will appear on several pages so if you haven't written it down don't worry").
Links in handouts / documents
If you're giving people a handout with lots of links then to save them typing each one individually a 'master' link can help here. As above, add all the links to a page and then share the link to that page. There's no need to replace the other links, people will like to see all the options and then know that they don't have to type them all in. A single link is a useful addition here, rather than a replacement as in slides.
You can also use link shortening for any individual link in your document, particularly those that are long or stretch over one line. In documents that are emailed the link may well 'work' but part of it might be cut off so the person is being sent to the wrong place. Not everyone knows to copy and paste and 'reattach' the broken address so it's helpful to pre-empt this by shortening the link first.
Getting more information from the link you've created
If you use bitly.com to shorten your links then you can see how often it's been clicked on (or typed in) - this means that you can get an overview of traffic to that page - but only the traffic that has come via your shortened link. You'll get no information about other routes in to the page.
2. Shorten links like a pro
Customise* your link.
Always customise. Ironically short gibberish links are probably worse than long ones that are comprehensible. In the example above I shortened it to 'URLette' (small URL) but the default one would have been a meaningless string of numbers and letters. Certainly quicker to write down, but not necessarily easier - use actual words if possible.
And for advanced users...
Go meta - one link to rule them all
Share one link which takes people to a page where they can find all of your mentioned links
Take your list of links, add them to a page. Take the address of the page and shorten / share that.
When sharing this single link on your slides make sure you shorten it and customise it so that it's easy for your audience to clock it quickly and write it down during the talk. It's also helpful to highlight verbally what you've done and why because there will be others in the audience who might be at future risk of giving lectures with unnecessarily long links. Teach them :)
By convention links are blue and underlined but since your audience can't click on them you are not restricted and can display them as you please. You probably don't need to include the http:// bit but it can be quite useful in directing the eye to something that looks like a link, and for the same reason blue isn't a bad idea either.
I and your future audiences thank you for this consideration.
How I prepare presentations for giving talks (18 October 2014)
3. How to shorten your links
Go to any link shortener page, put your long link in and press 'shorten' (or equivalent) to get a smaller one. Take advantage of any customisable options as appropriate. On some (eg Bitly) you can sign in with Twitter.
http://is.gd/ (customisable (look for "Further options/custom URL") but no QR** codes)
http://v.gd/ (customisable, QR codes)
https://bitly.com/ (customisation, new QR codes no longer possible, log in optional)
https://goo.gl/ - Google (QR codes - add .qr to your generated link to get stats, but no customisation)
http://tinyurl.com/ (customisable, no QR codes)
@schrodingerskit reminded me that bitly links actually let you see the statistics relating to how often your link was viewed.
**QR codes - let people 'scan' your link from printed material
If you're going to put a link on printed material and want to save people typing things then use a QR code ('Quick Response') to let them use their phones' camera to go to the site without having to type anything in. If your URL shortener doesn't come with 'native' QR codes you can create them with other free services, such as http://www.qrstuff.com/
^For people who don't have a blog, some suggestions
There are numerous sites which let you publish a one-off page. That'll give you a link that you can then shorten / customise and share as before.
https://woto.com/ (formerly Cloudpage)
Storify's not bad either https://storify.com/
If you know of other examples tell me and I'll add 'em.