Is it considered rude to draft other random cyclists? On my commute to work, if there a cyclist in front of me, is it rude to catch up and draft?  To effectively draft I would usually need to be within a foot of their back wheel.

There are two situations:

Trainers
There is one part of the commute that is often used by individuals and groups of riders who seem to be training rather than commuting. Generally I would draft these guys if I can sprint to catch them.  As they are going quicker than I can sustain, I never take a turn at the front.

Commuters
I think any fellow commuter is probably ok to draft and if they slow down enough I'll take a turn at the front.
There was a post on this subject on The Guardian Bike Blog.

I think there are a couple of issues with drafting random cyclists:


it could be unsafe, particularly if they don't realise you're doing it.
some people will object to being drafted - it can be considered an invasion of your personal space.


I think your best bet is to ask before drafting, then there's no problem.