For starters, I have an iPad but find iOS tedious compared to Android. I mostly use my Nexus tablet in it's place. That said, they can basically serve the same purpose.
A lot of people I know play around with sketching on their tablet. For me, it's not as productive as paper sketches that get captured into Evernote when they're ready (more on that later).
If you work on interfaces, you need to be testing on an iPad. Whether you use it often or not, the market at large does. Like I said, I don't like iOS at all but I constantly check my digital work on it to see what my audience will see. Love it or hate it, device testing is a big part of the digital design process.
I held out for a long time. I carried around a print portfolio of my key work and process notes. People were always really impressed that I used such an old-world method of presentation: "A handmade portfolio!? Wow!".
But things changed when I tried handing over a tidy little tablet full of content (which I could update much faster) and let them flip back and forth while I chatted. The conversation was relaxed; things weren't so formal; the audience felt free to ask questions (not propose challenges or sit silently). The tablet was the way to go.
Evernote rules. I use it to capture everything in meetings and while I'm brainstorming. I've turned a lot of my compatriots on to it. Many of them like to use a tablet with a keyboard when they take notes. I usually just tap away on my phone, but I use the Nexus or iPad from time to time (with a physical keyboard on rare occasions). On any of those devices, it's also a huge relief to just snap a picture of the whiteboard or a napkin sketch or even my less technophilic neighbor's paper notes.
The thing my phone and/or tablet have most dramatically transformed is my mountain of little paper scribbles. The back of my Moleskine used to be bursting with scraps; they were scattered on my desk or in drawers; in whatever containers my car offered. Good luck tracking that stuff down. I scribble things everywhere. Having a mobile device of any kind around with a camera allows me to snap a pic into Evernote and then toss all that detritus. Text in images is even rendered searchable in Evernote's database. Problem solved!