The first question I would ask is, do you need the plugins to access the UI of your host application, or add any UI elements of their own? Or will the plugins be limited to querying and/or supplying data to your host app?
The latter is much easier and opens up two possibilities. Others have already mentioned DLLs, which is the first way to go. Certain caveats apply - in general you should be interfacing with a dll using only the data types that are used in Windows API. THat way you can be sure that the plugin DLLs will understand your data types, no matter what language/compiler they were created in. (So for example, use PChars, not strings. Do not as a rule pass Delphi classes such as TStream to a DLL. This will appear to work in some cases, but is unsafe in general, because even if the DLL was compiled in Delphi, it may have been a different version of the compiler, with a slightly different idea of what TStream is). Google for using DLLs in Delphi, and you'll find plenty more tips.
Another way that hasn't been mentioned yet is to enable scripting in your application itself. There are several very capable 3rd-party scripting engines, both commercial and free, and most of them allow you to exchange Delphi objects with the script. Some of these libraries support only Pascal as the scripting language, others will let you use Basic (perhaps better for beginner users) or other languages. See for example RemObjects Pascal Script (free) at http://www.remobjects.com/free.aspx .
My favorite scripting solution at the moment is Python for Delphi (P4D, also free) from http://mmm-experts.com/Products.aspx?ProductID=3 It can interface beautifully with your classes via RTTI, and allows you to execute Python code in your Delphi app, as well as use Delphi classes in Python scripts. Given the popularity of Python, this may be a viable solution if you want to attract developers to your project. However, every user will need to have a Python distribution installed.
It seems to me that the barrier to entry, from the point of view of potential plugin writers, is lower if you use scripting than if you choose DLLs.
Now, back to my initial question: things get much more complicated if you need the plugins to interact with your user interface, e.g. by placing controls on it. In general, DLLs cannot be used to do this. The Borland/CodeGear-sanctioned way is to use packages (BPLs). With BPLs, you can access and instantiate classes offered by a plugin as if they were declared in your host application. The catch is, all BPLs must be compiled with the same exact version and build of Delphi that your main application is. In my opinion this makes packages completely impractical, since it's hard to expect that all the potential plugin writers around the world will be using the same version of Delphi you are. A major pitfall.
To get around this, I have experimented with a different approach: keep using DLLs, and develop a syntax for the plugin to describe the UI it needs, then create the UI yourself in the host app. (XML is a convenient way to express the UI, since you get the concept of parenting / nesting for free.) The UI description syntax can include callbacks to the DLL triggered when the contents or state of the control changes. This method will restrict plugins to the set of VCL controls your application already uses or has registered, though. And it's not a one-nighter job, while BPLs certainly are.
Google for "Delphi plugin framework", too. There are some ready-made solutions, but as far as I know they usually use BPLs, with their limited usefulness.