I have to disagree with jessemhess his app recommendations. Let me elaborate.
Dailer One - Its ok, but not crazy about it. I use contacts more then the dialer so not much need for a T9 Dialer to me.
SMS Popup - Pointless. Handcent, Go SMS. and Go SMS Pro(Free despite the pro name) are the most popular text apps on the market by far. All 3 of them provide this function. It differs slightly only because it can use custom themes, and has a quick reply box with out the need for tapping a button for a quick reply box.
Dolphin Mini - It is a very popular browser, but if we are talking browsers that have to do the rendering all by there selves(explain in a sec), I prefer xScope. It has a few themes, but most importantly it is faster. It lacks the plug ins of Dolphin but most are useless to me, but has a better ui partly because the tabs dont hog screen space. In the end though I have switched to Opera Mini. Opera Mini is developed by the makers of the Opera browser for desktop. It can sync up with Opera to load all your bookmarks. I dont use Opera on the PC, but installed it anyways to manage my bookmarks for when I restore apps. Opera actually passes the web page to a set of dedicated servers that compress the website first before passing the data to your phone. Because of this it is by far the fastest browser on the market. Only thing it lacks is the ability to swype tabs by swyping the screen.
Adobe Flash Player - Well actually I gotta agree here.
Google Docs - This is an up to you app. Personally I dont use my phone for business and have no use for this what so ever. If my device wasnt personal use only then maybe I would.
Now let me list some must have apps. Now of course others will disagree but here is some more practical recommendations but a bit less customized to your needs. For that we would need to know what you need to do with your phone. Heres a few I can think of.
Go SMS Pro - See above. Plus it has an easy custom theme builder even an idiot can use. I matched it to the theme of my sig.
Titanium Backup - You have to root(aka jailbreak) in order to use this app. Rooting voids your warranty, but is easily undone in most cases should you need to return the phone. VZW will never know. This allows you to back up all your apps and data. If you get in to flashing custom roms(modified versions of android specific to your phone offering many performance enhancements and cool tweaks usually, such as better battery life, Over clocking which can improve performance but also at the cost of battery life). If you dont root and rom, dont really need it then.
Angry Birds - Theres are 3 angry birds games, each a little different and all very addicting! There free to Android users but iPhone uses have to pay
Amazon App Store - They give away free paid apps every day with life time updates of that app for FREE!!! It also has alot better sorting options and such then the stock market.
Battmonx Donate - I loath the idea of wasting space on a home screen for a battery widget. It places a battery icon in the notification bar that reports the battery percentage in 1% increments. I cant recall if the Inc 2 suffers from the battery issue the Moto Droids do where it reports battery in 10% increments only. If It does not then check out Battery Indicator Pro.
Beautiful Widgets - Hugely popular.Adds a bigger clock to your home screen with weather. Its themable. Also try Fancy Widgets and see if you like it more.
Flipclock Widgets are cool to. Pretty similar to fancy/beautiful widgets but includes system info to!
Dropbox - It requires a PC app but allows you to place files in a folder on your PC that is accessible via the dropbox app. I keep my titanium backups in here, and I keep back ups of rom zips here in case I would need them on the go for some reason. I also keep a copy of the Inverted Dropbox APK on my SD card. You can find inverted(black instead of white usually) apps in the themes forum. Never know when you could accidentally format your SD card and needs your back up apps and roms.
K-9 Mail - If you want to check your email on the go, this is THE app.
My Verizon Mobile - View your bill,minuets,text, and even pay your bill!
Opera Mini - Fastester browser on the market by far, kinda of cheats in a way, but see baove for more details.
PowerAmp - MP3 Player. Self explanatory, but I love the GUI and features. Theres free alternatives out there though.
TeslaLED - May or may not work on your phone, but some sort of flashlight app is a must have and this is by far the brightest! It turns your camera flash LEd on and off. Of course with it being so much brighter, I question how safe it is long term due to the extra heat emitted. Of course these "flashlight" apps are not supposed to be long term solutions anyways.
Titanium Backup - See above.
Google voice - Visual voice mail with transcripts. The transcripts can be pretty bad at times, but I think slowly they are improving. You can also use free wifi calling to, I think, and free wifi texting. You can also set up your google voice phone number(you can get voicemail only if you want) to be your primary number, and this way if you switch carriers, in which case I pitty you, you can take your gv number with you and not have to deal with porting the number. ATT tried to BS me and claim VZW would charge me for 4 lines if I tried to port my numbers.
lol I hope I didnt bore you to death! I tried to keep it a general must have apps list. If you have specific needs you can find specific apps for your needs. Just hit up the market, search and give any that sound good a try. You can usually find more then 1 app that does the same hting but you find you like the GUI of one more then the other.