When I started playing a year and a bit ago on play money sites, I used to consistently blow my tiny play money bankroll, but I have gotten a lot better over time as I have switched to real money
and my game has improved. There is so much more satisfaction in slowly building than wild swings which almost always results in being bust yet again. My personal bankroll rules are a bit complicated as I use a handmade excel file to track my results (I only play tournies), which can also tell me my average and maximum buyin, but as a standard rule for a moderately cautious bankroll management rule, this is what I would suggest...
Cash game: 40 - 50 buy ins minimum.
STT: 70 buyins minimum for reg speed, 100 for turbo and 150 for hyper. Spin and Gos
need more like 200 buyins.
MTT: 150 buyins minimum for reg speed, 200 buyins for turbo and 250 for hyper and bubble rush. More caution should be taken with larger fields (>1000) and less with smaller fields (<200).
Of course, you can always take a few shots at higher buyin things, if you don't care so much about the money then you can be less cautious, and if you really don't want to lose it then you can be more conservative, but I think that these are pretty good guidelines... Hope this helps...