Can Arduino be used in commercial products?
Since legal questions sometimes need really specific answers, I found Arduino's exact position on this:

Physically embedding an Arduino board inside a commercial product does not require you to disclose or open-source any information about
its design.
Deriving the design of a commercial product from the Eagle files for an Arduino board requires you to release the modified files under
the same Creative Commons Attribution Share-Alike license. You may
manufacture and sell the resulting product.
Using the Arduino core and libraries for the firmware of a commercial product does not require you to release the source code for
the firmware. The LGPL does, however, require you to make available
object files that allow for the relinking of the firmware against
updated versions of the Arduino core and libraries. Any modifications
to the core and libraries must be released under the LGPL.
The source code for the Arduino environment is covered by the GPL, which requires any modifications to be open-sourced under the same
license. It does not prevent the sale of derivative software or its
inclusion in commercial products.
In all cases, the exact requirements are determined by the applicable
license. Additionally, see the previous question for information about
the use of the name “Arduino”.

Source: http://arduino.cc/en/Main/FAQ
Disclaimer: Arduino's position on this may change over time, I'm not a lawyer and this doesn't constitute legal advice, blaa, blaa, blaa... :)  In short: I'm not responsible if you get in trouble.
Update: February 2021
The structure of the Arduino FAQ page has changed, but it looks like the main point remains the same.  The above text has been broken out across multiple sections of the &quot;Compatible Products&quot; section:

Physically embedding a board inside a project
Deriving design from Eagle files
Source code and LGPL
Arduino development environment (Slightly changed wording)