Bottom Brackets Similarities
 

Are all bottom brackets interchangeable with different brand sprocket and crank assemblies?

No. Some spindles are JIS taper, others are ISO taper. Generally JIS taper is from low to mid range japanese bikes. These are generally not interchangeble except under certain circumstances. Read all about it at Sheldonbrown.com For further complications, some BB have "thick" cups, some have "thin", and this effects which spindle and ultimately crank you may use with that particular BB, etc etc

http://www.bbinstitute.com/manual.ht...emo%20Chapters

http://www.sheldonbrown.com/bbsize.html

good places to start.

We can only dream

I've mixed up ISO and JIS bottom brackets and cranksets quite often, and never had a bit of trouble. If possible you should avoid it, but with shimano making such nice JIS bottom brackets for so cheap, it can be hard to resist.