Being early at the bag checkin and politeness helps a lot. I try to go
overseas to a new destination every year and do a credit card bike
tour. Before I had the folding bike it was at the mercy of the agent
at the counter. If the agent was a guy my wife would do the pretty
talking and it worked well most of the time :)
I also have read many times that when the agent ask what is in the
box/suitcase to tell them something like inline wheelchair, exercise
equipment and some other silly stuff. it seems to work for some.
However my folding bike suitcase looks pretty normal so I don't get
the question. Having a regular looking suitcase works well for me but
beware any bike traveling with you on the plane will receive the same
treatment as other bags, that is, bad handling. This is the reason I
kept the cost/investment of our travel bikes to a level I am
comfortable with in case something bad happens to them.
We also have done the rental thing and just took our saddle and pedals
from home and swapped them at the rental place, it worked fine but you
usually don't know how well maintained those bikes are. Depending on
the destination rental may be a great choice. We rented bikes in Nepal
and New Zealand. Nepal bikes where old but very well maintained, New
Zealand bikes they where brand new bikes (literally out of their
boxes) that needed adjustments as we went.
Carlos