World of goo- an oldie but it'll never be bumped off my list!
Grooh
Where's my water
Joining hands
Bag it!
There's many more, but I find that those 5 are of upmost quality graphic wise, with a fresh fun innovative concept and awesome puzzles to solve, but never too hard, and they never get boring, they keep adding new elements to keep the game fresh and fun.
Monsters ate my condo really should also be on that list, though it's only one mode so you don't get as much of a variety as the other 5 listed.
WOG is a classic, its what modern day gaming should be, sheer brilliance.
WMW- innovative idea that's fun and adorable, constantly being updated with ne content, never ending fun.
Joining hands has alot of levels, another very unique concept, I couldn't put it down, played for hours right through to the end. No more levels being added though, well so it seems..so that's a bummer
Bag it! Such a cool concept.. And so life like, we all go grocery shopping and it makes an everyday chore really fun. I only enjoy the puzzle levels and collecting badges and medals, not interested in the arcade modes. More levels coming soon too.
Grooh - my current addiction.. Very unique..kinda like a match 3 platformer with color changing elements..I'm in love with the grooh character too. And the devs said more levels coming very soon.
Notable mentions and why they didn't make it
Juice belts - no updates
Iblast moki 2 - no update despite more levels promised
Bumpy road - not enough variety or campaign mode
Saving private sheep - graphics a little sloppy
Zen puzzle garden - doesn't evolve enough
Zen bound 2 - doesntbevolve enough
Home sheep home 2 - not enough levels
Scribblenauts - not enough levels
Monsters ate my condo - not enough modes
Puddle puzzles - no updates, sloppy graphics
Triple town - only one mode, doesn't evolve much, lack of gameplay updates
Sploosh - not enough levels
Cut the rope - too easy and slightly over exposed..almost bored of it because it's so popular..kinda like getting bored of the Simpsons because you've heard all the writers jokes and kinda get over it.
Edit **
Ohh you said apps
The top 5 apps I used would be-
1. Soundhound - tells you what song is on the radio..you can even sing/hum the song
2. Photo editing
More beaut - photo editing app that lightens, brightens, smooths and tones your photos..and it's free
Photoshop free - I use to crop and sometimes contrast, exposure, etc
Snapseed - lots of different editing options
Plastic surgery stimulator- I use this just for the liquify tool to edit graphics and photos
With the combination of those 4 editing apps it gives me results just as good as photoshop on the computer, that goes for graphics and photos, though the resolution isn't as good obviously..but it's good for mockups or whatever when you don't have access to your computer.
3. Noteshelf - you take notes, draw, color, symbols, etc.. Better then I real notepad.. It's a simple app but I use it alot just as a note taker really, to do lists, grocery lists, reminders, doodling, etc
4. Messages from your angels - Doreen virtue - oracle card app that allows me to have guidance when ever I need it. Use this daily, brilliant cards, very accurate. I have 6 of her tarot card decks in real life.
5.splashtop - connect to your laptop or computer and control it from iPad.. I often do this when a family member asks me to show them how to do something on the computer so I don't have to even get up! Ha ha I'm lazy
Honorable mentions
Smule - play the piano with no actual talent! It's free
Pianist - play a mini piano and you van record your songs and stuff
Animation HD free - it's fun to make little animations

I draw certain phalic objects..really fun !
Appzap - it's already been mentioned or it'd be 1.. This has come in handy alotyou can set certain apps on alert for sales and updates
Testflight - be a beta tester for game developers straight through the app, no computer required
Atomic web browser - actually let's you download stuff which safari doesn't allow.. My bf often sends clips of his new song demos and I rarely go on my comp so I download them to my iPad instantly
Puffin - let's you view flash sites like pr0n and habbo!! <- this has COME in HANDy very much lol
Vidrhtym - Make a music video in 30 seconds..really awesome video effects and sound
Wicked unusual unique photo effect apps-
Toonpaint turn yourself into cartoon
Percolator - adds rings and circles into photo
Half tone - comic book
Wordfoto - turn photo into words
Photo tropedelic - psychedelic effect
Dicovr apps is good for discovering new apps or games..you type in an app you like and it tells you other stuff you'd like based on that app.
If you have a cat or dog you have to get " game for cats" or " paint for cats" my cats love it so much and full on go skits trying to catch the mouse..paint for cats actually makes the cats paw prints show up while catching the mouse and paints a painting and u can print it out it pit it on the wall. My cat is a picasso for sure !
"wreck this app" is really fun for people who are into art..it's a spin off of "wreck this journal"
It gives you instructions on each page like " get someone else to draw on this page" and "attach a photo and deface it" etc it's quite fun but not many pages for the price..
Torch apps do come in handy.. But I often just use the brightness of the screen as a torch nut if I need a proper torch that comes in handy
Every aplenty device needs some word games..7 little words (free), bookworm, and text twist and who wants to be a millionaire should all be on every single apple device, they never get tiring..I have had them for a year or more and they always get opened atleast once a week, still. Wordsworth hd is another good one.
I always have fun creating faces on "face factory" too..I'm a little kid in an adults body haha
Also, if your into sticker photo booth..this app called "photoframe dada" is literally the BEST sticker photo app I'm the world.list possibly even better then a real booth, it has hundreds of frames, confetti, stickers, font, pens, etc. I have spent countless shouts playing around with it, there is so many possibiltys seriously, and it's constantly being updated too.. Probably the most content ice ever got for 99c
If you have foxtel then the foxtel guide app is awesome..I always forget to tape a show then I will panic thinking I might miss it, then I get on the app and set the show to tape straight from the app..I wish u could delete other tv shows though cause if ur memory is full it still doesn't tape and that's annoying.
Words with cheats - I usually use this to make a good first word..if words with friends starts off with a short word the game doesn't evolve much cause there's not much to build off..so yeah if I'm ever stuck on the first word I cheat and make a big first word for the benefit of both me and the other player lol, but sometimes I also have to peak if I'm totally stuck. It comes in handy.