Since I began using smartphones in 2004, they've become an indispensable part of my daily workflow. When I bought my first iPhone (a 3G in 2008), that workflow changed immensely, and for the better. The wide variety of apps available for the platform and the connected nature of the tools Apple provides make iOS a very compelling choice for managing many aspects of our business.
At Nickelfish, I do a lot of different things, but a large part of my daily routine is maintenance of all our systems, both user desktops and laptops as well as our online accounts, backups, and services. I use a combination of apps to manage all of this easily. 1Password syncing to Dropbox means I have all the information for everyone's accounts as well as software licenses and secure notes at my fingertips. I use Screens to monitor a few different machines via VNC around the office, making sure backups and updates are running and completing, and test machines are still testing the way we need them to. I use a variety of Dropbox-linked text editors to take and refer to notes throughout the day, notably WriteUp and Elements on iOS and nvALT (a Notational Velocity fork by Brett Terpstra) on my MacBook Pro.
I'm currently using iCloud for my contacts, personal calendars and a personal email account. But we synchronize our company mail, contacts, and calendars with a Google Apps business account, so we're set up with the standards on everyone's Macs. Apple Mail and iCal run all day, and we all have those accounts hooked into our phones too. We used to run iCal server off of our Xserve internally and had our mail hosted externally, but we made the decision to bring everything together into Google Apps several months ago because of the availability of apps plugging into it. iOS has a ton of different calendar apps that can either sync with Google or with the iOS calendar accounts, as well as apps that tie into Google Docs, so people can choose how they want to hit those services, and there's definitely something for everyone.
When I'm out of the office, I rely on a few of the iPhone's heavy hitters - Mail and iMessages - to stay in touch, as well as a few fantastic third-party apps. I use Verbs for IM when I'm away from the computer, since work doesn't always stop at 5pm each day, and I've begun using a combination of Captio (see my Pick of the Week) for dropping to-do items in my inbox and the new Reminders app with Siri when I either can't or don't want to use my hands to remember something. I'm currently using WeekCal in place of the iOS default calendar because of a few great calendar views I prefer, but that seems to change on an almost weekly basis (no pun intended).
Ultimately, the best thing about using iOS to keep everything moving is that there are so many choices and so many ways to get things done, I can always switch things up if I get tired of an app or need new features. My 3G use is relatively modest, so I've also recently made the jump from a grandfathered unlimited AT&T data plan to a 4gb Data Pro with tethering, so that I can more easily stay online when we're out at meetings with limited or unavailable wi-fi access, which happens all too often. Hopefully this allows me some more freedom as I continue to rely on iOS to make all the things I'm currently juggling stay in the air.