Which one ?

I'm happy with the Targus stylus. It gets a lot of use (and is passed around a lot) and is still going strong.

"Essential" accessories are pretty individual. The accessory I use the most is the Apple Composite AV Cable. I use the cable to connect my iPad to a digital projector. I show videos and use the iPad 2 as an Interactive White Board with Note Taker HD (which supports "TV Out"). I've also used Key Note to deliver presentations. I thought I would use the Apple Digital AV Adaptor more often. This adapter supports display mirroring, but it turns out that HDMI hookups are still quite rare. Still, I sometimes use it to connect my iPad to my monitor (in my case via an HDMI to DVI adapter).

I have the Camera Connection Kit, which I use to transfer pictures and video from my camera when I travel. I have a Belkin Micro 2.1A car charger to keep the iPad going during long car trips (my spouse's game playing would otherwise flatten the battery). I have a Tom Bihn Ristretto bag that goes everywhere with me.

Finally, I have the OtterBox Utility Series Latch. It gives the iPad 2 a strap so it can safely be used one-handed. It also has a lanyard attachment so the iPad 2 can safely be used while walking around or by a child. I'm not 100% happy with the Utility Latch - it covers and slightly interferes with the volume and power buttons and the audio jack. It is also not compatible with the Smart Cover. Imperfect, but it is the only easily-removable strap/lanyard combination I've found.