Note

 
All application names & icons link to their page at AppShopper.com, a brilliant free app directory service that is much easier to browse than the iTunes AppStore.

You can also create an (anonymous) account there, which enables you to automatically keep track of the apps you want or own and get informed about price changes and updates. Saved me lots of money already!

They also have helpful rankings of all categories and consolidated lists of what's new or on discount. Check it out!

All links will open in a new window or tab.

Office & Productivity

Some of these apps have evolved so much that they've replaced several others I've previously used in one go, particularly the document readers. So, this is the only category list that got shorter instead of longer...
Documents To Go Premium. Nobody should have to use Microsoft Office, but reality is sadly different. So, if you are one of the unlucky ones, at least this app makes your Office portable. Documents To Go Premium lets you EDIT, create and view Microsoft Word documents, Excel spreadsheets and Powerpoint presentations. You can also view PDFs, Apple iWork and other files, though not necessarily as well as with Readdle Docs or GoodReader. A free desktop app (Win & Mac) enables proper non-destructive two-way file synchronisation via WiFi.
JotNot Scanner uses the iPhone camera and clever image processing algorhythms to scan multipage documents, receipts, whiteboards, business cards and notes into PDF files you can email directly or upload to Dropbox, iDisk/WebDAV, Evernote, Box.net, or Google Docs where they can be shared with others. Even integrates with Google's OCR engine to upload an editable text version of your scans into a Google Docs account. Useful for lazy people like me, who can't be bothered to type up notes, posters or flip-charts...
ReaddleDocs is a revolutionary document viewer that can catch documents from any source: Windows, Mac or Linux computers, web sites, email attachments, iDisk, Dropbox and other online file storages. All files are saved locally so you can read them anytime, anywhere! ReaddleDocs combines a network file server, online storage client, web browser, file manager and robust document viewer all in single application. Absolutely essential when you get that the iPhone is not just a phone. This app is the perfect all-rounder for all kinds of documents; for PDFs I also recommend the next one.
GoodReader is an advanced PDF viewer, way ahead of any competition. The handling and reading even of huge files (100MB) is superb and the PDF Reflow feature extracts pure text from PDF files and automatically wraps words, so all of the text fits to the screen perfectly without you having to scroll horizontally or zoom in and out. Files can come from your computer, the internet or email attachments. It also integrates with MobileMe iDisk, box.net, MyDisk, Google Docs and Dropbox. Fantastic! I use it to read books and magazines (the Rainbow Bridge!) and to always have my own publications & designs with me. (Almost everything these days comes as PDFs.)
Callway: Super Fast Smart Dialer is the only, really smart dialer that offers everything with speed and style. With its all-in-one display, your favorites, recently dialed contacts or the dialpad is a touch away. Not only does the T9-like search find contacts and groups quickly, it lists them using a unique an intuitive analysis technique based on usage patterns learnt over time and the available info for a contact (amongst several other things) to give you extremely relevant search results.
Groups: Drag & Drop Contacts Management, Group Email, Smart Contact Filters, Map Contacts. Groups takes contacts group management to a totally different level. With a highly innovative user interface, you get to manage your contacts in a way the iPhone sadly can't by itself. The feature set is too long to list here, but the most important feature for me is the ability to search your contacts by keywords in the contact notes. (From the makers of Callway and 2Do)
2Do is a stunning (Best User Interface 2009) ToDo List with Push notification and iCal synchronisation. ToodleDo sync is supposedly coming soon, as well as integration with other services. I had a much more expensive ToDo app before (plus an even more expensive Mac companion application), but switched to 2Do (despite iCal being a bit dull) because it's so pretty and fun on the iPhone that I actually want to to do to do lists! (O.k., too many to dos here...)
Dictionary is an intuitive, consistent, talking (high quality text-to-speech), hyperlinked and integrated English illustrated Dictionary and Thesaurus, Spell checker, Vocabulary builder and Wikipedia browser. There's even a Rhyming dictionary. Optional Translation of words being looked up to Spanish, Italian, French, German and Japanese (translation uses Google translate and requires an internet connection, the normal Dictionary does not). There is a multitude of dictionaries in the AppStore of varying quality and cost. This one beats them all and has replaced four other apps I previously had. Simply the best!
iTeleport: Jaadu VNC, awarded "Best App For Remote Desktop Access" by O'Reilly, lets you control your desktop computer anytime from anywhere. Supports Mac, Windows, Linux. See your computer screen and control its keyboard and mouse from wherever: a few feet away, or even halfway around the world. One of my most expensive application but brilliant! If I'm on the road and really need a file, I can remote control my home computer to email the file to me, check whether an upload/download has beed completed, surveil running processes or even my room by turning on the webcam...
1Password Pro will securely store important information and can automatically log you into websites with a single tap. There's no need to remember the username, password, or even the website address. With the ability to save and sync encrypted text notes, credit card numbers, and similar information to the Mac companion software, this is an essential tool for everyone dealing with lots of sensitive information. (Without the Mac application, I'd be lost in my web work. Now I have all the data always with me!)
Billings Touch takes the Apple Design Award winning time tracking and invoicing experience from the Mac and puts it in your pocket. It does work as a standalone application but really only makes sense as a companion to Billings on the Mac, which I can recommend (it's what I use).
iBank Mobile lets you track your day-to-day spending and monitor account balances on the go. It's easy to enter and categorize transactions, track expenses, or view running balances. Desktop users of iBank for Mac can also sync transactions, account information and categories automatically and seamlessly to iBank Mobile. Then update your transactions as you work, shop or travel, and sync new data back to iBank, for perfect personal finance management.
iOutBank Pro allows you to manage your accounts from different (German) banks easily and securely. Based on the accredited German safety standards HBCI and FinTS your encoded account data will be transmitted between your bank or your thrift institution and your iPhone using a secure internet encryption (SSL/HTTPS). There's also a free one-account-only light version named iOutBank. For German banks only! Most UK banks (e.g. NatWest) have their own free apps in the UK Appstore.
ShoveBox Mobile helps you catch and sort all those small scraps of information that you can't immediately act on but would rather not forget. It's a proper mobile note-taking app on its own, but what makes it really worthwhile is that it wirelessly and automatically syncs with it's Mac version, which is one of the best information management utilities I ever got.
Evernote turns the iPhone into an extension of your brain. From notes to ideas to snapshots to recordings, put it all into Evernote and it gets instantly synchronised with your desktop. If you make photos of text (e.g. business cards), the Evernote server even does an Optical Character Recognition, so the text in the picture (!) becomes searchable. This is one of those applications the iPhone was made for. Incredibly, Evernote is still free - at least the basic service, which is enough for most people. You owe it to yourself to check out this application, both on your phone and your desktop. One of the most useful things ever!
Measures is a unit and currency converter with a huge database of almost 1000 units in 38 categories. Because it also has normal calculator functions, it has replaced the iPhone's built-in application for me. The great thing is that you always see both units at the same time, so while you're (e.g.) calculating prices, you can see them in two currencies at every step. Very easy handling and many customisation options. Indispensable!