Is Nikon D3000 (DSLR) compatible with a speedlight?

Guys, Is nikon d3000 compatible with a speedlight?

Yes, but pay attention that it's a new one. The old ones that were made for film cameras use high trigger voltages that might fry your camera.

Of the Nikon ones, the SB-400, 600, 700, 800 and 900 will work perfectly. In case of third party manufacturers i'd recommend that you ask the question again with the specific speedlight being mentioned.

Yes, but as Jens said - old flashes (made for film cameras) can have high trigger voltages that can fry a digital camera.

You can check various models of flash here;
http://www.botzilla.com/photo/strobeVolts.html

Pretty much any Nikon speedlight will be ok, as will any modern digital flash.

Your D3000 does NOT have the Nikon wireless flash system (CLS) so the only way to control an off camera flash is to either use your pop-up as an optical trigger (off camera flash will need to have an optical slave mode - not all do), or to get a set of radio triggers (RF602's are good, £25 for a set).
Off camera, the flash power will have to be controlled manually.

If you get a Nikon speedlight and use it ON camera, you will have TTL (auto flash metering) available.

Edit: I would not recommend the SB400 - fairly underpowered and no swivel head nor manual adjustments which makes it pretty useless off camera.

Yes you should buy this one

Nikon SB-600 Speedlight Flash for Nikon Digital SLR Cameras

Easy-to-view LCD with 6 simple-to-understand backlit buttons
FV lock holds flash value, enabling recomposition prior to shooting
Accurate i-TTL flash control achieved through flash exposure monitoring control
Ready light located beside the LCD on the back panel - highly visible even when used as a remote
Auto zoom of 24 to 85mm, extendable to 14mm with built-in wide-flash adapter