What I use my Galaxy Nexus for:
1) Making calls. Stock Dialer application in ICS does this fine. No need for an app.
2) Texting. Stock texting app in ICS is fine, but ugly and barebones beyond belief. Which is fine, because most (all), of the non IM platform specific apps think we're all teenage girls or something with the amount of crap they try to throw into their app. I admit, I'd probably be willing to pay money for a simple, elegant, fluff-free texting app. After hours of searching app stores, reading top ten lists, etc, I've concluded I am a weirdo and that my approach to texting is an abomination or something.
3) Maps. Google maps on Android is great. Don't need a third party app.
4) Email. I use gmail. Which is on the phone already. So, no need for a third party app. Work email uses Lotus Notes, so I use Lotus Notes Traveller for that. I've been toying with the idea of setting up my Lotus Notes account to auto archive emails and forward them to my gmail account. I hate Lotus Notes and their ridiculously small email quotas.
5) Shopping list. I go food shopping roughly once a week. Sometimes once every two weeks. I use Out of Milk for my shopping list. It's free, and you can jot things down on a computer at work, or wherever, and it'll sync with your phone. It's about the simplest, non-clutter-filled, list app out there. If you're OCD, you CAN spend your life categorizing things if you want to, but for those of us who just want to jot something down fast without spending ten minutes going through options and menus and categories and tags and...etc, Out of Milk is great.
6) I sometimes listen to music. For that I use Pandora. The Pandora app is ugly as sin due to the ad placement being designed by a very stupid person, but luckily I don't look at the app, so much as listen to it.
7) Taking pictures. I use Lightbox + Camera app, and upload via Picasa.
8) As a flashlight. I use Flashlight HD LED. If your phone has a flash for its camera, it's pretty amazing how much light you can get by using it as a flashlight. Whether it's bad for your flash to stay on, I don't know. But, it's been very useful when fumbling for keys in the dark, etc.
9) Google Translate. This app has pretty much completely demotivated me from bothering to learn other languages. I've even had some success with simply holding it up and letting someone speak, to then have it translate what they're saying to me.
10) Google Sky Map. Shows/tells you what you're looking at as you point your phone to wherever you want. Makes me regret the hours and hours and heck, days, and weeks, I spent memorizing constellations and other objects in the sky when I was young. I've lost street cred with other amatuer astronomers, but I'm too old to care.
11) Swatchmatic. This app is essentially a color palette maker. Point your camera at whatever, and it will come up with a palette based off the color you're pointing at. It's a quick and easy way for me to get a start on color choice for web design.
12) Workout Trainer. Free workouts delivered in a not so horrible machine voice with animations and timers. While I've had my daily routine for most of my life, it's been interesting to mix things up with a different workout once or twice a week. They're all bodyweight/dumbbell workouts that don't require being in a gym.
13) I do have several news apps on my phone, but I'd be lying if I said I actually used them on a regular basis. I find myself in front of a real computer/laptop often enough during the day that I just never bother reading the news on my phone.
14) Google Wallet is something I've tried to integrate into my life with mixed results. On the one hand, it's pretty amazing how many stores where I live have the Mastercard Paypass system, thus I'm able to use my phone to pay at the majority of places I shop. On the other hand, both my debit and credit cards are Mastercards that work with the Mastercard Paypass system, and there's really no efficiency gain in me using my phone to pay for an item over pulling out my debit card and waving it in front of the terminal. I suspect if I didn't have a Mastercard, it'd make a lot more sense using Google Wallet.
15) Evernote. Not so much to take notes, but to access notes I've taken on a desktop/laptop.
16) Juice Defender. Unless you're a smartphone luddite, or have bought a larger battery than what came with your phone, or are using a Motorola Razr Maxx, your battery is likely going to just barely last a full day. Battery management does wonders to increase the odds you can get through a day comfortably without charging your phone. Juice Defender is my app of choice in that regard.
17) Automatic actions is usually the domain of an app called Tasker. Lately, I've been giving on{x} a try. Surprisingly, it's a Microsoft product, though they don't go blaring that out in any way. It's also very much a work in progress, but I really like their approach to task automation over Tasker's. What is task automation? As an example, you can have your phone text anyone who calls you while you're driving, "Unable to take your call. Driving.".
18) I've also tried to integrate Google Now into my life and largely failed. The premise is great, but execution is weak. If you're on Jellybean (maybe on ICS too?), swipe up from your Home button. It doesn't help that while Google can obviously pinpoint my location perfectly on Maps, etc, that it's obvious it must be using wireless Mac addresses for locations that it uses to give you data in Google Now, and that there is nothing more frustrating than Google Now giving me info pertaining to a city I am not in, while showing me in the correct city down to the correct building in Google Maps. As much as I love Google, they have always been very bad at integrating all their products together smoothly. I mean, how many damn messaging apps do they have-each of them with a feature or two that the others don't, despite all using the same account, forcing me to use all three rather than just one?
Sorry, totally getting off subject.
The one last thing I wish I had working on my phone, but had to give up when I switched over to Tmobile's rather insane (as in, why in the world would I stay in my $100/month contract when Tmobile's $30/month pre-paid fits my needs better), pre-paid smart phone plans, is Google Voice. I miss my visual voicemail.
Though, to be fair, I tend to ignore 99% of my voicemails these days, and just assume if it's important, people will text or email me.
I could just use a Google Voice number as my main number, and then get Google Voice to work with my phone, but I've had my regular phone number so long that I just don't feel like dealing with "changing" phone numbers.
Things I don't do on my phone:
1) Play games. Maybe I'm just an old fart, but I fail to see the appeal of playing games on small devices. Nevermind my complete lack of interest in games that are essentially from 90s era tech when played on a PC. Yea, I'm so excited.
2) Watch videos. Same reason as #1.
3) Browse the internet. Same reason as #1.
4) Read ebooks. Same reason as #1. Plus, that's what my basic Kindle is for. Which can also fit in my pocket on some of my pants. Now, if only I could get rid of physical keys.
My random thought about smartphones that's bugged me for years?
Why in the world won't a manufacturer that isn't Apple make a phone with solid parts (ie: not all plastic). I think Apple products are largely horrible, except I am always impressed by their ability to make their hardware not feel like a cheap piece of plastic. I suppose I'm basically immensely down on their software, while high on their hardware (though I do think their phones have always been too small).
Is it the weight? Because, I think weight is the last thing anyone really cares about concerning a phone (ie: if a phone is too heavy...you have issues).
Is it the cost? How much more could it possibly cost to use some metal or other alloys that aren't plastic?
I guess this is very similar to the PC issue, where PC manufacturers seem to refuse to make quality shells for their laptops. Plenty of them try to emulate Apple in the brushed metal, but it's usually poorly fit into plastic chassis or something. It drives me nuts. Surely there must be a market for PCs that aren't built as cheap as shit without having to pay someone several thousand dollars?
This is an issue I simply can't wrap my head around. The closest thing to a well-built Android phone that doesn't feel like a plastic toy is the Motorola Razr with its kevlar build. I love Android from a software perspective. But, the hardware design that houses all that excellent software over the years has kept my inner self curled up into a ball wailing quietly to myself like a little girl.