I recently asked this question of a few developers I know and was surprised by how few of them had any developer-focused phone applications. I use several apps regularly for dealing with development tasks when I'm away from my desk:
Dropbox lets me share files between my various machines and devices so I can keep notes, technical documentation and reference books on hand, wherever I am. In addition, I use PlainText so that I can edit text files in Dropbox while I'm on the go. I can take notes, write "offline"
blog posts and edit "local"
copies of project wikis, since I keep copies of my github projects' documentation in Dropbox.
For remote server management, I rely on the Cisco AnyConnect VPN client and the TouchTerm ssh terminal app. These let me connect to servers in our secure data center or out in the cloud and perform general maintenance and troubleshooting operations at the command line.
Finally, for project management on the go, I rely on the Github Issues and Unfuddle apps, for my free open source projects and my company's projects respectively. These applications let me create, review and comment on tickets on all my projects, wherever inspiration strikes me.
I'm not sure there are that many actual apps for developers, but there are plenty that make my life as a hybrid much easier. I work for Sprint and we just got the iPhone, so I'll concentrate on what makes being mobile easier. Reminders iPhone app is great at making nice simple lists for meetings. Adobe Connect is useful for attending the actual meeting on mobile. Of course, Skype is handy for calling in to a meeting. I love iThoughtsHD for mind mapping, and OmniFocus for keeping me just that, focused. I use Numbers, a spreadsheets app, all the time and also Bento, a project management/event planner app. Evernote is an essential app that connects your notes/code to all other desktop/iPad/iPhone/Android versions of the application. Dropbox is another essential app because I always want my files available.
Keynote is a must-have app for me, and iAnnotate PDF is a great application for marking up PDFs. I use YouSendIt to send files, and plain old Notes automatically syncs with my machines, so I can write CSS anywhere I go. I find SketchyPad and iMockups the most useful of all. They are both wireframing iPad tools, and in seconds I can create wireframes for web or mobile while in meetings.
Sketchbook is a great drawing tool and I have a stylus to make it easier. The wireframe mockup tools are not a good workflow for me yet. Keynote is great for organizing presentations for clients. In fact Gusto and FTPOnTheGo are getting closer to being quite useful. Granted, when I pull those out on the road to do remote development, you'll also find me pulling out a wireless keyboard.
We use AnalyticsPro to watch our site analytics. We also use GitHub in our development so we find the Issues app for GitHub very helpful. When it comes to taking client notes and working budgets, we swing between Documents To Go which can work with Google Docs, and the iOS versions of Pages, Numbers and Keynote.
For organizing our thoughts, we use SimpleMind+ and Wunderlist. They allow us to create mindmaps that are portable and lists that can be accessed from multiple locations.
Beyond that, the best of what exists in mobile is in the browser. Sometimes you just don't need an app; you just need a browser and connectivity.

