Note: This answer has been updated due to changes in Trello. Legacy information still available at the end.
You can link to other cards in any board. Just paste the link to the card into the text...
and Trello will convert it to a nice-looking link with an icon and the card title.
When you open a card the address bar changes to a direct-link to that card, so you can copy it from there. This does mean that you have to navigate to the other card in order to get the link. The old way allowed you to start typing '#' and then choose from a list or type the number. However, it does mean that you can link to cards on other boards.
The old way
Yes, you can! All you have to do is type
xx is the card number - as far as I know you can do this anywhere that you input text - I have tested it in descriptions and comments.
For example you might have something like this in a card description:
- Card #23 (Tidy shed)
- Card #4 (Clear out garage)
- Card #45 (Do that other thing)
#xx will appear as a link to the referenced card.
Note that the card reference is working only in the same board, it is not cross-board
Response from Trello (2016-01-27)
When the old behaviour changed I filed a bug report with Trello and got this back:
What you discovered is actually an expected behavior at this point. We recently deprecated the number linking functionality within Trello, and at this point, unfortunately, there is no such feature available. Right now, your best bet is to use the full link to the card.
We definitely understand that that's frustrating. I'm sorry that we've removed a part of Trello that was important to your use of the product. Unfortunately there were some issues with the links and they wouldn't work properly once cards have been moved to other boards. Similarly, our mobile application would only show the number and wouldn't actually build a clickable link.
The best I can say is that we're working to change how we add things to Trello so we don't have to remove features in the future.