for my XPERIA X10 (running Android 1.6)

1. Google Maps: Fairly obvious, but still brilliant
2. Dolphin browser: Nice gesture support, though its speed isnt amazing
3. myPlayer: iPlayer on my phone
4. Sky : Allows me to remote record to my Sky box
5. London journey: Gives my bus and tube routes across London

So those basically won't be useful to anyone outside the UK....

Well in that case...

(On my iPhone 3G)

• AroundMe (If I need directions to a restaraunt/movie theater/whatever... this app has got me set)
• Pandora (I'm always listening to Pandora Radio, and now I can do so on thShe go! Love it!)
• AP Mobile (Great news App that's entirely customizable and even notifies you when something important happens)
• Netflix (Just finished watching some Futurama on my iPhone. Awesome)
• Shazam (What is that song? I must know?! Well now I can know)

Here's some fun ones:

• Plants vs Zombies (It contains the entire single player game and most of the mini-games... for only 3 bucks. Amazing value!)
• Ocarina (I can now be like Link!)
• I am T-Pain (Everyone needs an Autotune app!)
• Angry Birds (Only a dollar, and it has amazing value and is completely addicting)
• Cyanide and Happiness (Laughter on the go)
• GeoDefense/GD Swarm (Tower Defending goodness)
• Fatbooth (Never gets old making people fat. Never!)
• TowerMadness Zero (its free, and its an awesome TD game. What more do you need?)

Damn Droid doesn't support Netflix.  It only has Blockbuster.  Aside from that, I have all of the Apps listed in the first half of your post.  I REALLY hope Plants vs Zombies is available for Android.  The 360 demo was too much fun and I'd love to own it.

Reset Generation  <- the best handheld game ever, always fun

Evernote  <- as it says, remember everything

AntSnes  <- very good SNES emu

Heroes Lore  <- Quite memorable journey it was, no wonder it's the most famous korean game

Dance Fabulous  <- Dance Floor on your mobile, I was suprised by how well the game works

P.S. Shazam never worked properly for music I like

iPhone:

iTeleport/Touchpad - iTeleport is a VNC client with a great interface and some snappy features. I mostly use it to administrate servers, and it really takes the sting out of midnight server admin when you can do it from your bed. Touchpad is basically the same app except it leaves the screen blank so you can use it as a wireless touchpad to control, say, a media PC.

AppAdvice - App news, app reviews, app guides, and an app price watcher. Figure out which of the many apps in any given category will best suit your needs and keep track of great bargains on software.

Elements - A simple text editor that syncs up with your Dropbox account. Great for taking notes and generating rough drafts.

Air Video - Stream videos from your PC to your phone. Is that video in a format that's too tough for iOS to handle? No problem. Air Video will transcode almost anything into .h264 on the fly so it streams to your phone faster and is easier on the battery.

TuneIn Radio - The ultimate streaming audio app. Comes with tons of channels (even my local community radio!), varying bit rates, options to pause and record, and information about songs and programs when available.

As a bonus, all of the above apps except TuneIn are universal, which means I get to enjoy an iPad optimized version for no additional fee. I use TuneIn too, since the lack of an iPad-optimized interface doesn't do much to hamper a streaming audio app.

Since this is a gaming site, I'll follow Smeags' lead and post my 5 favourite games (excluding ones he's already covered):

Glyder 2 - A nice, relaxing flight game about collecting, exploration and the occasional race. Some compare it to Pilotwings, but I confess I've never played Pilotwings. Careful management of speed and altitude brings a novelty to the flight mechanics.

Skies of Glory - A WWII flight sim that's not so relaxing. It has decent of content and some fun online multiplayer. Also some of the most stunning visuals I've seen on the platform.

Osmos - Sort of a physics-based arcade puzzler reminiscent of Orbient. At it's basic level, you eat things smaller than you to grow bigger, and avoid things bigger than you. But of course, things quickly get much more complicated. You need to be aware, you need to be precise, and you need to strike the right balance between patience and decisiveness.

Jet Car Stunts - This game is like TrackMania if the cars came with a rocket strapped on. You need to keep strict control of your orientation, altitude, and speed if you don't want to re-enter the earth's atmosphere...

HookChamp/QuickHook - 2D adventure platformer that dares to ask: What if Indiana Jones could swing around like Spiderman? Simple controls and good physics yield extremely challenging gamplay.

android 2.2

appbrain 

dropbox

remote for itunes

google voice

launcherpro 

do a search for faad and openfeint... they have a free game/ap a day and they do it for both iphone and android...

faad has some really good ones at times.... only up for one day (i missed the day they had puzzlequest on grrrrrrr.)

There's so many times when I wish I'd had shazam...