As Eben Upton has often said, Arduino and Raspberry Pi don't really compete significantly because they're so different (maybe just 10% overlap). They should instead be regarded as complementary. When the rather meagre hardware interfacing of the Pi is not enough for your project, combining an Arduino with your Pi will often provide a very effective mix of extensive low-level interfacing and high-level programmability.
However, traditional Arduino boards are based on 8-bit microcontrollers, and although these are perfect for a huge range of applications, there are times when it is desireable to use an ARM microcontroller when interfacing with the Pi's ARM1176, and not only for ARM symmetry. Some things are simply easier to do with a 32-bit processor, and if processing speed matters in your application then an ARM microcontroller will almost always leave the 8-bit micro way behind.
Unfortunately your options become somewhat limited if you want to use an ARM microcontroller board yet still want to enjoy the ability to use Arduino "shields", the many hundreds of daughterboards that can plug into an Arduino board's headers and which make Arduino such a singularly impressive ecosystem. Although the Arduino organization will soon be releasing their own ARM-based Arduino Due using an Atmel SAM3X8E device (a Cortex-M3), it's not officially out yet (despite having been sighted on flickr), and not many third parties have tackled this empty spot in the market.
The best known are probably the Maple from LeafLabs http://leaflabs.com/devices/maple/ , and the Olimexino-STM32 from Olimex http://www.olimex.com/dev/olimexino-stm32.html which offers quite a lot more and yet is cheaper (£16.96 from Farnell). Both are based on an ARM Cortex-M3 from ST, and offer a degree of Arduino header compatibility.
Well, this area is about to be given an interesting shakeup, courtesy of yet another ARM licensee, Freescale. Their Kinetis KL25Z Freedom Board is now on pre-order at Element 14:
- http://www.element14.com/community/community/knode/dev_platforms_kits/element14_dev_kits/kinetis_kl2_freedom_board
- http://uk.farnell.com/freescale-semiconductor/kl25z128vlk/board-kinetis-l-series-kl25z/dp/2115294?COM=freedompage_knode ,
and you really can't go wrong at its board price of £8.10 + Arduino header form factor . 
Admittedly the Kinetis KL25Z's KL2 microcontroller is a Cortex-M0 which is the little brother of the Cortex-M3, but for hardware interfacing that will often be more than ample and is still a huge step up from the 8-bit AVR. What's more, it's highly likely to undercut the price of Arduino's about-to-be-released Arduino Due, so things may get quite interesting in this market niche.
[Added note: the Kinetis KL25Z board uses uses a Cortex-M0+, not M0 -- see post 16, ]
For expanding the Pi (and the BeagleBone too) into the Arduino niche, the Kinetis KL25Z looks extremely good to me. Admittedly, it won't provide anything like the power of an STM32F4-Discovery board which uses a Cortex-M4 http://uk.farnell.com/stmicroelectronics/stm32f4discovery/board-eval-stm32f4-discovery/dp/2009276?Ntt=STM32F4-Discovery , and at £9.96 from Farnell this Discovery is the very clear price-performance leader. However, the Kinetis KL25Z has the Arduino form factor, and that may make all the difference. YMMV !!
Very interesting times ahead! 
And just in case that isn't tempting enough, ST's Discovery range has a Cortex-M0 version, the STM32F0-Discovery http://uk.farnell.com/stmicroelectronics/stm32f0discovery/eval-board-cortex-m0-stm32f0/dp/2096251?Ntt=STM32F0-Discovery which is even cheaper at £5.88. If Arduino headers aren't essential but you want the cheapest possible Cortex-M0 board to expand your Pi, beating £5.88 on sheer price will be very hard. It's fairly safe to predict that the Cortex-M0[+] range is going to have a colossal impact.
Morgaine.
