When I got my Android smartphone, I was looking forward to all the cool apps I could put on it. Then I discovered the cruel reality that you have to pay for apps (lame) or allow them to show you ads (super lame). At least the ad-laden apps are easy to spot since they all require the "Full internet access" permission, so I can reject them with extreme prejudice before installing them.
Anyway, since I'm cheap, and I hate ads (which is why I use a DVR to skip TV ads, and FireFox to block web ads), I've been forced to dig deep to find decent apps that are both free and ad-free. There aren't many, and most of them are crappy. Nevertheless, here are the hidden gems, the ad-free free Android apps I have on my phone right now.
File Expert (Geek Software Technology)
Really, Android should come with a file manager of some kind. This kind of omission is just silly. File Expert does the job, though the user interface is clunky (copy/pasting and other operations require too many tap-and-holds and too many sub-menus). It also puts itself in your notification bar, which is annoying (I hit Back repeatedly to exit completely and get it out of the bar). For ad-free and free though, I shan't complain.
Nudnik Calendar Notification (Amit Moran)
By default, Android only vibrates once when you have a Calendar reminder come due. Useless. This led to a lot of missed reminders until I installed this app. I have it set up to constantly vibrate, forever, until I acknowledge the reminder. Android should do this out of the box. This ad-free, free version is crippleware (many features locked out), but I don't miss reminders any more so it's 100% functional for me.
Mine Message (Lei YU)
Same as Calendar notifications, Android only vibes once when you get a text message. Again, useless, and the cause of many missed messages. Like Nudnik, I have it set to vibe forever until I read the message.
Moon+ Reader (Moon+)
Android can read text and html files, but using the web browser to do so is a pain (remember, there's no file manager, so you have to type a big long nasty URL to get to every newly added document). The display and search capabilities of the web browser are also limited. The other feature I really, really like on a reader is auto-scroll. That's where the text scrolls slowly by (at a user-adjustable speed) so you don't have to hit any buttons or swipe the screen to "turn" pages. Turning pages is so 19th century. Moon+ addresses all 3 needs with no ads and at no cost. The main menu is kind of clunky (a few extra taps that are really not needed to get to my docs) but on the whole it's a darn good app.
Replica Island (Team Replica)
Fun little game. Very difficult to play with the touch screen, fortunately I have a slide-out keyboard that works quite well for control.
Just found this one today. Shame I'm too cheap for a data plan, so I can only watch when I have WiFi access.
Brightness Widget (Sisedi media)
Color smartphone screens are difficult to see in daylight yet are so bright they hurt my eyes at night. To adjust brightness takes a tap, a scroll, and another 4 (yes, FOUR) taps with stock Android. Ridiculous. Try doing all that in sunlight when you can't see the screen, or at 3AM when the screen is blasting your dark-adapted eyes with the visual equivalent of a theater spotlight in your face. This app (or rather, widget), lets you define three brightness presets -- night, indoor, and outdoor. Then you put it on your home screen and tap it to cycle through the 3 settings. Since you know right were the icon is, you can tap it "blind" in sunlight until you can see the screen.
MotoTorch LED (Ryan Alford)
This is neat. The built-in camera has a "flash", which is just a high-brightness LED. This app (with Widget mode) simply turns it on solid so you can use it as a flashlight. It's surprisingly effective, probably a good 10-20 lumens which is more than enough to navigate indoors or in the woods (maybe not so great with city light pollution). As a widget, it's easy to get to by just tapping the icon on your home screen, no sub-menus and junk to fiddle with.
ColorNote Notepad (Notes)
When I first got my smartphone, I found myself composing a lot of emails to myself so I could jot down notes. This takes care of that ugly kludge by allowing fewer taps to enter a note and easy retrieval of notes all in once place instead of scattered in my Inbox.
WiFi Buddy BETA (Andre Rabold)
There are a ton of WiFi apps out there, this one probably isn't the best but it works well enough that I can't be bothered to look for another. Shows a list of available access points and lets you tap on one to connect. Simple and effective, though a little buggy.
Ad-free free Speedometer
Yes, that's the name. I am so obsessed with ad-free, free Android apps that when I wrote one myself, I named it as such. Yes, I wrote an Android app. :) Stock Android will tell you your speed via GPS, but it's a torturous path to open My Tracks, start recording a track, and switch to the details screen to see the speed in little tiny numbers. Not that you should be operating a phone at all while driving, but this is particularly dangerous. Also, I don't like the privacy concerns of software recording my whereabouts. My app just shows the speed in great big numbers as soon as you tap it's icon, and that's it. That's pretty much all it does. Oh, eventually I will upgrade it to read in MPH, km/h, and knots, save your top speed, display your compass heading (N, NE, E, etc), and allow different display color schemes, but for now it's just a simple free speedo with no ads. It's not in the Android Marketplace, because it would cost me like $30 to publish it there (remember I'm cheap, and I won't be making any money from an ad-free free app). So if you want to use it you'll have to tell your phone it's OK to install apps from "untrusted sources" and download it from here.