I have not found a strength training app that I really like all they way around just yet. I've tried quite a few, and my observations are listed below. My current solution is to use Google Drive for my training spreadsheet and Fitocracy Training app to log the work.
JEFit is a decent general purpose app with a focus on body building. Out of all the offerings, this is one of the closest to what I want but it does have some major shortcomings. In JEFit, KG and LBS are just labels, so if you ever travel and enter stats in the unit you don't normally use it will throw off all your charts. Same with competing, if competitions are held in a unit you don't normally use, you have to do the conversion yourself or throw off your charts. It's programming is good for weekly training. If your routine fits a nice weekly pattern it's perfect--but if it's a monthly or longer cycle JEFit's programming falls very short. Adding ad hoc exercises is a bit of a pain, so simply not using the programming part is rather annoying.
Fitocracy Fitness Tracker App is great if all you want is a way to track what you are doing today. It doesn't pretend to have a programming aspect, so it makes it really easy to record things ad hoc. I use Google Drive for my training spreadsheet and the Fitocracy app to record the work. This combo seems to be good enough. Fitocracy does know the difference between a pound and kilogram, so if you ever have to change units it won't mess any charts up. Problem is, you can't have one exercise in KG and another in LBS if your gym has mixed equipment (most commonly with kettlebells).
Multi-Year Training App this had a lot of potential, and I paid for the programming add on--which was a waste of money. The app can handle more complex programs if you use the ones that are built in, which includes strong lifts, starting strength, Wendler 5/3/1, German Volume Training, and a few others. It provides some good primers on strength training out of the box, but the piece meal purchasing for things that should be included (like tracking your work) is not cool. The programming essentially is limited to one day's work. Each day is it's own program. You can't even string a week's training together. Really. It's a waste of the $1.99 to get the programming. I'm sad I spent money on it. If you use the packaged programming, it's workable.
Big Lifts only does Starting Strength and Wendler 5/3/1. Don't waste your time if you ever want to do anything besides those two. It doesn't support ad hoc exercises, or track any assistance work you do.
Gym Hero at the time I tried it was nothing more than a digital notebook. I could track my work quicker and easier with a pen and paper. It does integrate with RunKeeper for historical tracking, but the strength training portion doesn't get sync'd with Fitocracy if you use that.
Another possibility I saw that integrates with RunKeeper, but I have not tried would be Fitness Tracker 90.