I’ll just list out a few of the apps I have right this moment. If an app costs money, I’ll try to list out some free alternatives. Hopefully you’ll find that they’re useful!

Instant Messaging:

IM+ ($) [iTunes Link]

IM+ supports Live/MSN, Facebook, GTalk, Yahoo, and many more. Also supports push notifications. It’s a little pricey for an IM client at $10 but it’s one of those apps that will stay with you.
Free alternatives: IM+ Lite or eBuddy

Social Networking

Facebook [iTunes Link]

This is the best way to browse Facebook on your iPhone or iPod Touch.

Entertainment

Flixster [iTunes Link]

This is a great app that lets you watch trailers for new and upcoming movies and releases, view the Rotten Tomatoes or Flixster rating, and even finds the nearest theatres and movie play times. Facebook and Netflix integration is also supported.

Midomi SoundHound ($) [iTunes Link]

Identifies songs recording a short clip or listening to you sing or hum!
Free Alternative: Shazam

News

iReddit ($) [iTunes Link]

The iReddit app lets you view Reddit articles, upvote and downvote, post replies, and subscribe to different subreddits. The free version is ad-supported.
Free alternative: iReddit Lite

Navigation

AroundMe [iTunes Link]

AroundMe finds points of interest around you. Browse by type such as Banks, Gas Stations, Hotels, Movie Theatres, Restaurants, etc. and it’ll show you the distance from your current location. Great when you’re in an unfamiliar area trying to find something.

Shopping

eBay Mobile [iTunes Link]

The eBay mobile app lets you search, bid, and pay for items.

Utilities

Photoshop.com Mobile [iTunes Link]

A good free offering that lets you edit and apply effects to your photos.

Wikipanion [iTunes Link]

A light Wikipedia reader.

Dictionary.com [iTunes Link]

The best dictionary I’ve seen. It stores the definitions on your phone or iPod so you can search even when there is no internet connection. Dictionary.com can also play the pronunciation (internet connection required) and does Thesaurus.com.

ConvertBot ($) [iTunes Link]

There are many free unit converters on the app store, but I think this has one of the nicest interfaces. It’s similar to a classic iPod with a scroll wheel to select your unit type. Complete with animations and sound. I’ve had the most fun converting units ever.
Free Alternative:  Convert Units for Free

Delivery Status Touch ($) [iTunes Link]

Expecting a lot of packages? Deliveries lets you track each item and displays them in a very pretty view. It supports Amazon, Apple, Canada Post, DHL, UPS, USPS, and many more. (Full list)

iSSH ($) [iTunes Link]

iSSH lets your SSH into some server and also supports VNC. Very useful if you need to remotely administrate something.

Dropbox [iTunes Link]

Dropbox (for Windows/Mac/Linux) is a service that lets you store files and lets you sync them across several computers. With this app, you can access files such as photos and documents that are in your Dropbox as well as upload photos from your iPhone.

Backgrounds [iTunes Link]

An app that lets you easily browse and download backgrounds that fit for your iPhone.

Games

Implode! ($) [iTunes Link]

Try to blow buildings up by strategically placing different bombs.

Tap Tap Revenge 3 ($) [iTunes Link]

Music game with free and paid tracks.
Free Alternative: Tap Tap Revenge 2

Jailbreak

These apps are available in the Cydia store for jailbroken iPhone or iPod Touch users.

Backgrounder

Lets you run apps in the background. Hold the Home button while an app is running and you will enable backgrounding for that app. Hold it again while the app is running to disable backgrounding. This is useful if you need to switch to another app for a little bit and need to go back quickly. There is an indicator on the backgrounding app’s icon to show that it is still running. Remember that leaving too many apps running in the background will reduce battery life and memory.

SBSettings

An extremely convenient way to change settings without going into Preferences.app. Just swipe the top bar and you can enable or disable 3G, EDGE, Bluetooth, WiFi, kill processes, and change brightness – all without leaving your current app.

3G Unrestrictor ($)

Tricks apps into thinking that you are connected via WiFi. Useful if you want to download large files from the App Store over 3G, view higher quality YouTube video, or use VoIP apps. Includes an SBSettings toggle.

Rotation Inhibitor

An SBSettings toggle which lets you enable or disable rotation for apps like iPod and Safari.

If you have been having as much fun as I have wih the iPhone apps, then there is no doubt that you’ve come across numerous apps that deserve no more than a few launches. After a few weeks of looking for the best iPhone apps, here are some that I found are genuinely awesome (in roughly the order of appearance on my phone).

This article will be constantly updated as I find more great apps.

Palringo [iTunes Link]
As of the time of writing, this is the only free IM app on the store and it works pretty decently. Its interface is slightly cluttered and you need to make a special Palringo account to use it, but once it’s set up it’s a good app.
See also: Meebo (Web App), IM+

1Password [iTunes Link]

I own the 1Password application for Mac and syncing my data between the computer and the phone is seamless. Setup is easy, interface is beautiful, and overall, really handy. As far as I know, you don’t need the paid desktop version to use the iPhone app.

Facebook [iTunes Link]

I have this app for one feature only: mobile picture uploading. Everything else is just icing on the cake. If you don’t need a dedicated facebook app, then you may be interested in just Facebook’s mobile site.

Twitterific [iTunes Link]

The ubiquitous twitter client sports a really clean interface plus a ton of integrated features.

Remote [iTunes Link]

Even though I don’t need to use a remote for my iTunes library that desperately, this app’s installation simplicity and concept makes it a keeper just in case.

Last.fm [iTunes Link]

Last.fm is really handy when you finally become tired of your 16gb of music. I just wish there is a scrobbling feature like from the jailbroken days. (And yes, I am aware that Apple won’t allow background processes.) You’ll need a free Last.fm account first.
See also: Seeqpod (Web App)

Shazam [iTunes Link]

Shazam uses the microphone to record a sample of some music and identifies it for you. The coolness of this app and potential handiness makes it a keeper.
See also: Midomi

Evernote [iTunes Link]

The iPhone app lets you take text, picture, and voice notes and sync with the desktop version of Evernote. Free Evernote accounts have a 40MB limit but that should be plenty for text notes.
See also: YouNote

Movies [iTunes Link]

Possibly the most feature packed movies app I’ve seen so far. Movies shows you upcoming and current movies, theatres near you, newly released DVDs, and more. It even plays trailers!
See also: Showtimes

Zenbe Lists [iTunes Link]

A simple but elegant list app that syncs with Zenbe online.

weDict [iTunes Link]

For some reason, the app store of weDict is not as polished as its jailbroken precedessor, but the basic features are there. By default, it includes the Wordnet 2.0 and English Chinese dictionaries. More dictionaries are available via jailbreak.

Urbanspoon [iTunes Link]

Urbanspoon is a really nifty app (that actually works in Canada) that locates you and finds the restaurants near you based upon your preferences.

LocateMe [iTunes Link]

This little gem finds your location and lets you see a bunch of points of interest including banks, gas stations, hotels, movie theatres, restaurants, supermarkets, and a lot more. Its results are from Google so entries include the address and phone number which you can easily use to map or call.

Wordpress [iTunes Link]

Could be handy if you have a Wordpress blog! There are no formatting options so its features are rather limited, but it does allow picture insertion.

Wikipanion [iTunes Link]

A simple and elegant Wikipedia application that optimizes Wikipedia entries for the iPhone screen.

Radiolicious [iTunes Link]

FlyCast streams internet radio and podcasts. The streams are optimized for Wifi/3G and EDGE.
See Also: FlyCast Mobile

iVote [iTunes Link]

A fun little app which lets iPhone users from around the word voice their opinion on different subjects.

a2z Pro [iTunes Link]

A simple but effective unit converter.

Tap Tap Revenge [iTunes Link]

Tap Tap is a music rhythm game where you have to tap or shake according to the “notes” that appear on the screen. Somewhat similar to Guitar Hero and Rock Band.

Aurora Feint [iTunes Link]

A very polished puzzle game with RPG elements. It’s rather intense on the battery but still highly recommended.

Sol Free [iTunes Link]

Sol Free is an amazingly polished solitaire game. Currently, it includes the following games: Baker’s Game, Demon, Klondike Deal 1 and 3, and Spiderette.

So that’s it! If you feel that you have a better free alternative, feel free to leave a comment.

Scramboni [iTunes Link]

Scramboni is a really entertaining multiplayer word descrambling game.