First there's Unit Conversion gratis version. The program's main menu has the categories presented in a large and clear light gray font on a black background. The program has a good numpad of its own and doesn't use the default virtual keyboard provided by the system. What bothers me, however, is that when you enter a category there's no usable default conversion selected. Instead the selected conversion is something like "km -> km", i.e. it does nothing. You also need to press "convert" instead of seeing the conversion result change as you type in more numbers. So, all in all not too good.
Second, we have aUnit Converter Free. It also has got a keypad of its own but in addition to that the default Android virtual keyboard pops up if you click the number field. The program is green text on black background -- some people apparently think it's cool but I'm not too fond of the scheme. The program does neatly operate in just one screen as there's first the category selection drop-down box, then the number field, and then the input unit, converted value and ouput unit. So, OK.
The third program is ConvertDroid. Compared to the previous two programs it boasts a way larger number of unit categories: 46. There are, for example, typography, fuel consumption and radiation related units available. The user interface of ConvertDroid feels rather crammed as it tries to display all available conversions at once. You don't select the input and output units from a list but instead just click on the number field for the desired input unit, begin typing and see the result of all conversions immediately. The program uses the default Android keyboard and as a slight annoyance it displays it in the letter mode by default, forcing you to tap it once to switch to the numeric keypad. The program does have a reasonable selection of default units visible in each category and you get less often needed units by clicking "Show all". Not too bad, but the keyboard-thing is annoying.
Next on the list is the cleverly named Unit Converter. The program has a very polished look with green "Web 2.0" icons and black text on white background. As the only program in this selection it has got a button for swapping the input and output units, which is a nice feature. You can also save your most often used unit conversions in the program's Favorites category which is shown at the top of the list. The program also converts currencies, loading up-to-date information from the web on the fly. I like this program, and the only annoying thing is that you have to hit enter or "Convert" to see the conversion result, i.e. it doesn't convert as you type. I might also want to have the categories as a drop-down list at the top of the screen but I'm not too picky on that.
Then, the pithily named Converter. The program operates as pithily as it is named: there are three drop-down boxes, two number fields and a "Clear" button (if you so choose -- you can also hide it from the settings). There is also a separate view for the categories as well but that's not needed at all as you can change the category from the main view as well. I like this one as well. It's simple and plain but has a very decent selection of categories and units. It even does number base conversions, which many of the other programs don't do.
Second to last, we have ConvertPad. The first thing you notice about the program is the insane amount of unit categories: 89! You can do conversions regarding viscosity, entropy, cooking and image resolution, to name just a few. This program would probably be your choice if you had a degree in theoretical physics, astronomy and some third subject as well. For anyone else it seems like an overkill.
Finally, there's another program named Unit Converter. Unfortunately this program also has the questionable honor of getting the last place in this comparison as well. It can only convert units from six different categories, not including such an obvious choice as speed. The Android keypad covers the target unit at least on my phone so at first you only see the "Value" field, "Convert from" text and drop-down box and the "Convert to" text, but not the drop-down box! The program also doesn't have any sensible default conversion values set but happily converts from, say, centimeters to centimeters. When you hit "Convert" the result slides in and you need to hit the Back key to get back to your number field and drop-down boxes. Due to all these little annoyances this program appears almost unusable to me.
There! Now the only thing left is to present the previous information in a nice tabular format. I hope this helps you pick a converter program -- or why not pick two: one for every day use and the other for the odd chance that your life would depend on correctly converting furlongs per fortnight to some sensible unit. ;)