Apps reviews and lists are ubiquitous, so why add my opinions? Because I have not seen a collection of apps on a single list that seem to be "general purpose", to address users going about all of life's varied activities.
I use my iPhone all the time. First thing in the morning, while still in bed, to last thing at night, the iPhone is a tool and toy that serves many purposes. Here is just a list and explanation of my apps, order of utilization, sort of:
The iPhone camera is my favorite tool. Any review will tell you how good it is. Because I use it so much, I also use other imaging apps. Adobe PS Express, TiltShift Gen, Camera+, Iris and Genius Scan all let me do specific post processing that makes the camera more fun, and my pictures more entertaining, I hope.
Mail, the native iPhone app, followed closely by the Gmail app. Mail handles all 5 of my inboxes well, but Gmail lets my use its label system to organize.
Beejive is the way to use chat apps like Gtalk on the iPhone. I also use WhatsApp for the same thing, to suit another person with whom I like to be in continual Gtalk contact. This is messy, but works, though if iPhone worked better to keep Gtalk running at all times, I would not use it.
Pulse RSS reader. There are three redundant ones I use, Pulse, Mobile RSS, and Google Reader. That is the order of my preference, based on how enjoyable they are to use, and the ability to link news stories in Twitter, Email, etc.
I use a few Twitter clients, including Twitter's. I like Seesmic best, only because it is easy to do searches. I haven't figured out how to easily search on Tweetdeck, though it is a smooth interface.
I use the native Calendar, Phone, Messaging apps all the time.
I use Blogpress every day to make blog entries offline and publish them when I want. I can draft several posts ongoing, and stage them to keep my blog updated once a day.
Docs to Go is essential for Excel spreadsheets that I use as data bases and to track expenses in my budget file.
Evernote replaces the native notes app, and is cloud based so I can use it from my laptop. This is where my lists, projects and more involved notes reside.
Remember the Milk is what I use as a basic To-Do list. It is more powerful than that, but I like it better than others I have tried. Most are really hard to use. That Apple has no native app for this requires all kinds of weird work arounds using Notes and Calendar, and is appalling.
The use of my iPhone for mapping is one of its most remarkable features. Beside the native mapping program, which is quite handy to find things locally, I added Motion X's GPS Lite and GPS Drive, fantastic apps that amaze me every time I use them. Also, the Starbucks app, and Free WiFi. I also use Around Me, and the native compass. A cooler compass is Commander Compass Lite, it makes me feel like a commando in a video game when I use it.
The native calculator works fine, but I like RPN calculators and more power, so use PCalc Lite.
I have Facebook and Linkedin, but use them infrequently. They are really nice apps.
I use tideApp whenever I go fishing.
For aural entertainment, it is Pandora and TuneIn Radio to go with the iPod.
The YouTube app works well, and I marvel at it when I use it.
Kindle is the reader for me, and I am reading the memoirs of US Grant now.
There is a handy app from Columbia called WHatKnot. I like and use knots. What can I say?
For football, I like College FB and Football Live! The are great.
Bing is something I use occasionally and try to like.
LightOMatic lets me use my LED as a flashlight. Cool and useful.
Also, Box.net, Dropbox for big file access in the cloud.
Games? I actually use the iPhone for games daily. WordPops, AC-130, Gun Range, Moxie, Word Shaker, Words Free, Sudoku, Solitaire, Word Warp, and my faves, FS5 Hockey and Osmos. You gotta try Osmos.
Thats it, a long list of apps that really make the iPhone more fun and functional.