Also, I wouldn't say that anything is a "competitor" for the Arduino, as long as it is still in the spirit of the Arduino and is open-source based...
I don't think the Arduino considers other manufactures as competitors, but the arduino will always be in competition for users, the true source of their success. Lose too much support from your existing or future user base and you will fail. So far Arduino has been very successful at building a large and growing user community and I don't see anything else attracting the same number of users over a similar time scale. There are products and groups that I have found interesting sense the arduino started up, but none seem to have gained the same traction that the arduino platform has:
Propeller chip, it's certainly a different kind of cat.
TI MSP .50 cent chip, $5 board.
Many ARM based modules approching or at or under $30.
Picaxe, lower start-up cost then arduino.
So there are potential 'competitors' on the horizon, but so far the Arduino team has managed to avoid pot holes large enough to slow their popularity. But make no mistake, the Arduino 'movement' could flame out in time as there is no guarantee that past performance will dictate future success.