More than occasionally, I have friends and colleagues asking what apps I use a lot on my iPad (or iPhone), and what I would recommend for this or that. While each is to their own, and your mileage may vary, I thought I'd start to capture some of the main apps I use and like here so that people can check them out and download if they like. And, no, I don't get any commission or kick-back for these recommendations, nor do I take any responsibility if you buy them and don't like them. :)
Notability
Note-taking on the iPad is a very individual thing, so I'm a bit loathe to recommend one note-taking style over another. That being said, Notability is a pretty comprehensive app. You can introduce pictures into your text, annotate them, use handwriting if you wish, sync with Dropbox, create folders and categories - there's not much it doesn't do. You can even record audio notes! Well worth the couple of bucks to buy it outright.
Toodledo
For a long time, Apple didn't have any kind of task list on their iDevices. Then, with iOS 6, they released Reminders, and while it's fine(ish), Toodledo is better. I find it very useful when you're following the GTD methodology - with contexts, projects, notes etc. - and it has a (not very pretty) web interface that it syncs with as well. Importantly, the Windows client also syncs with Microsoft Outlook, which is rare! Another outright purchase, and well worth it in my opinion.
iTap RDP
This one is a little geekier, but if you have a virtual desktop at work like I do, or if you know how to enable Remote Desktop connections to your Windows PC (Google it!), then this app is invaluable. It allows you to access your Windows PC desktop on your iPad as though you were sitting in front of it. You then use finger gestures to emulate the mouse and you basically have a fully-functional Windows desktop environment on your iPad, when you're on the same network. If none of that makes any sense, then steer away from spending the $16. But if you want to remote in to your PC, this app is the best I've come across.
Dropbox
I assume you already have this. And know what it is. If you don't, then head on over to Dropbox.com and sign up. Now. It's the best way to sync files from your PC or Mac with the 'cloud'/internet, and with your iPad. Go. Now. Install. It's free.
Paper by FiftyThree
Ever wondered why you can't use your iPad or iPhone while you're wearing gloves? It's because the iDevices utilise a 'capacitive display' - i.e. when you touch the screen, your finger is actually acting as a conductor and forming a capacitor which...oh, never mind. It means that drawing on your iPad is tricky because you have to use your (relatively blunt and squishy) finger. If you buy a stylus to do some drawing, then it will also be blunt and squishy. But that doesn't mean you can't make cool drawings on the iPad. Case-in-point: Paper (by Fifty Three). It's free to download, although you pay for more drawing tools, but it is a very beautiful app. Good for quick sketches.
TripIt
If you travel internationally at all, this app is great. TripIt is an online itinerary management site, and it's fantastic. When you receive your itinerary from your travel agent, you can just forward it to plans@tripit.com, and then all the details are loaded up and synced with this app on your iPad and/or iPhone. Great place to quickly reference flight numbers or hotel details.
This is another one in the 'surely-you-already-have-this' category, but on the odd chance you haven't heard of it, Flipboard was built for the iPad. You customise it with channels and social feeds, and it then it presents those items in a beautiful interface akin to a social magazine. Check it out - it's free. And awesome. It's frawesome!
Slideshark
If you PowerPoint a lot and find that whenever you view your slideshows on your iPad, the formatting is all screwy, then SlideShark is worth checking out. The app uploads your presentations to their server, converts them, and then syncs them back down to your device with animations and most fonts intact. Don't use it for work presentations that you're not allowed to upload to an external service though.
Downcast
Why would anyone pay for a podcast management app on their iDevice? I mean, Apple already has an awesome podcast app built-in, right? Well, I prefer to say that Apple has an app called 'Podcasts' built in. I leave out the awesome bit. Downcast provides a lot more flexibility and control to those of us who are podcast-junkies. You can get it to automatically refresh feeds when you arrive or leave a location, you can control which podcasts it downloads with what frequency, you can stream directly - the list goes on. Well worth it, in my opinion.
LogMeIn
They're a little less awesome since they started placing some restrictions on their free service, but LogMeIn is good for remote access to your PC or Mac when you're not on the same network (i.e. over 3G or wireless from somewhere other than your house.) And for the non-techies out there, this is a lot easier to set up than remote desktop connections. And it is free.
So, there's a starter for ten. If you have any thoughts or other recommendations, drop me a line or a tweet. If this is useful, I'll try and post another list in the future too.