Alright, after owning my Evo for over two months now (and recently rooting/ROM'ing/Kernel'ing it), this is my current list of must-have, recommended apps:
AdFree
Came pre-installed with Myn's Warm 2.2 RLS5 ROM, but I probably would've eventually got around to installing it. I've hated ads on the internet since the beginning, and I've been on the internet since before it was called "The Internet".
Alarms (PalmarySoft)
This is a port from PalmOS app called PalmaryClock. It's a great alarm clock app and I've been relying on it for years. The Android version doesn't have as many extra non-alarm related features, but the main alarm function is even more reliable in Android than it was in PalmOS.
aTAKEphOne (ShSh)
Another port from PalmOS, this is a dialer app. The i-Bar is the main feature of this app that makes it so useful. There's also a free 3rd-party i-Bar widget that's very useful. If you didn't use this app in PalmOS, you may not find it so "must-have" for Android.
Barcode Scanner
I use this and the Shopper app. I've tried most of these types of apps out there, but stuck with this one for reasons that evade my memory now.
Cover Art Downloader
I use the stock music player, so this app is very useful to me (but may not be to others). I first downloaded this app after trying PowerAmp music player which really messed up my cover art -- this app resolved the problem easily.
DirecTV
Because I just don't watch TV, I DirecTV. Haha. Only useful if you have DirecTV, and even then you can always just go to the website to remote schedule your DVR.
Documents to Go (Paid)
Another port from PalmOS. It's a relatively expensive Android app, but was about 2x the price as a PalmOS app. There may be better Word/Excel/Powerpoint apps out there, but this one does a great job and I've been using it on various platforms for about 6 years now.
Dolphin Browser HD
Although I like the stock browser as well, Dolphin HD is just plain slick. I really like the gesture feature and the UserAgent setting is more reliable than the stock browser. Being able to set the UserAgent for desktop and having Flash support has eliminated the need for me to have a lot of dedicated apps (unlike all my iPhone friends).
Droid FTP
Because I'm old-timer from way back in the DOS days, I still need a FTP client.
ES File Explorer
Like most people I started out with Astro, but after trying ES File Explorer I liked it better. The built-in network LAN share browser feature with my WinXP network was seamless and painless. And it's pretty.
Facebook
Yeah, I know. It's not really necessary to have the Facebook app with the great Android browsers that are available, but it's quick and nice to use every once in a while, just like Friend Stream can be. More often than not, I just access Facebook through Dolphin HD.
GPS Status
A new app for me. I was having GPS trouble the other day. A utility like this really should have come on all Android phones.
gStrings
Great app for tuning any string instrument -- for me it's a violin.
KeePassDroid
This is a password safe. Surprisingly, none of the three I used on PalmOS were ported over to Android, so I had to start from scratch. This was the best free one. I didn't feel like paying for another one only to have one of the PalmOS ones eventually ported and have to start all over...again...and pay for it.
Lookout Security
I don't know how well the virus scanning part works or if it's really even needed, but finding the phone features are great. I'm currently using the free version.
Nook
Since being a previous PalmOS user, all of my eBook library was in eReader. eReader did finally come out with an Android app, but it's still in Beta (after like a year) and is rather spartan. Barnes & Nobles bought out eReader.com and my wife bought a Nook, so it made sense for me to just witch to the Nook app. Unfortunately, although the Nook device can read eReader eBooks, the Nook app cannot. But I figured out a way to convert the eReader PDB's to Nook PUBs, so everything is working good now and I'm completely switched over to everything Nook.
NoteEverything
None of the PalmOS note apps were ported over to Android (so far), so I had to start from scratch again. Found NoteEverything to be the best for me.
PicSay Pro
If the Evo supported USB hosting, since I found this photo editor I probably wouldn't use my desktop computer except once or twice per week. This offers excellent basic photo editing features. I just have no way to get the photos from my DSLR's SD card to the Evo without USB hosting. Does great things with the pics from the Evo's built-in cameras.
Pimlical Android
The calendar apps on Android are inadequate to say the least. It doesn't help that the ones on PalmOS were so good. Finally Pimlico ported over their DateBk app to Android, and it's now called Pimlical. Great features, best calendar app available, and you support mountain gorillas when you buy it. That's just win, win, win.
Ringdroid
Great app for making your own custom ringtones, alarms, and notifications ON the phone (no desktop transfer required). Key features are the custom alarms and notifications, because for things like calendar events a "ping", "doink" or "chime" just isn't going to cut it for me. This allows for a MUCH longer notification sound or music. Love it.
RockPlayer
Plays every video I've thrown at it and works very well. The stock Android player works well, too, but RockPlayer plays more formats.
SetCPU
Must-have for anyone rooted. SetCPU and a custom kernel has given my stock battery double the typical charge life.
ShootMe
Great screen capture app. It says it's only for rooted phones, but it worked fine on my Evo even before I rooted it.
Shopper
Great scanner and find lowest price type of app. The biggest problem I have with this app is that I forget that I have it, so I'm still making purchases without checking to see if I can find it cheaper elsewhere. DOH!
SuperUser
Must-have for anyone rooted. Usually the rooting process (if it's a one-click root type of thing) will automatically install this app for you.
Time Recording
This is a great timesheet application for anyone with an hourly type of job. I used a similar app on my PalmOS phone, and although this isn't from the same developer it was so similar that there was zero learning curve.
Titanium Backup
Great backup application -- a function I was missing from the old PalmOS days of syncing and backing up to SD cards. Never really was comfortable with this whole Google cloud thing, but I'm getting there. Titanium Backup also allows rooted users to "freeze" and "thaw" apps or even delete them from the ROM -- no more Sprint bloatware! Great app, but be careful!
Touch Calendar
This was the calendar I was using before Pimlical/A was released. I still use it though because Pimlical doesn't have widgets yet. This is a great basic calendar app with unique UI where instead of switching between various views (day, week, month, etc.), you pinch zoom. Great for quickly checking the calendar for available dates or daily itineraries.
WeatherBug
Was using The Weather Channel app, but the latest update runs all the time and drains my battery, so I switched to WeatherBug. I'm glad I did -- I should've been using WeatherBug all along, it's just a much better and more reliable app. I still use the HTC Weather/Clock widget, but WeatherBug is more customizable.
Wireless Tether
Now that I've rooted, I also have free access to Sprint Hotspot, but Wireless Tether seems to be the better overall app both for individual as well as group tethering. It only does 3G, but most people don't find that to be too much of an issue. EDIT: It's been pointed out to me that both tethering options can do 3G & 4G -- can't remember/find where I read that Wireless Tether couldn't. Sorry about that bit of misinformation!
Hope this helps other Android/Evo noobs out there.