Aluminum arrows, and bow risers are anodized. Arrows are heavily loaded, way beyond what a frame is. I wouldn't worry about it on a frame. Easton one of the big providers to the cycling industry uses a lot of anodizing, but I don't know what they use for bike tubes, since if it is to be welded, it wouldn't be pre-finished. As Falanx says, it has come up as a stress riser, and people criticize it on rims. So you take your best bet.
Marine wise, it is ubiquitous. US navy does a lot of good things and a lot of bad things. Cost is a big part of that, but they use both highly disposable stuff and stuff that is really expensive. Certainly anodization is used heavily in yachting as is stuff that looks like epoxy coating.
What is the norm on cycling parts? Seems like a lot of parts look anodized, but they tend to be thicker section than tubes just for starters.