Then you weren't weight training right. Using a proper load, and a full range of motion on all exercises, especially compound movements, is one of the easiest ways to increase your functional flexibility. In other words, don't blame the weights, blame the weight lifter.
With that said, if you want to stick to bodyweight exercises, I'd recommend having some kind of squat, some kind of press, some kind of pull, and something for the abs each workout (gee, kinda sounds like a well-planned weight training routine, huh? That's not a coincidence.)
So a workout could look like: Squat or lunge variation, some push-up variation, any kind of pull-up or chin-up, and 1 (maybe 2) ab moves.
The biggest drawback with calisthenics is the fixed load (your bodyweight), and if you're looking for strength, you won't find the gains you want if you can do more than 10 or so reps of a given movement. Use exercises which challenge you enough to keep the reps to below 6, and you should be golden.
I know that Mike Mahler had a bodyweight routine on here a long while back, and you may want to check out Shugart's interview with Coach Sommer here: http://www.t-nation.com/readTopic.do?id=512003
It discusses gymnastic moves, which would be a great addition to a bodyweight program.