I live in a 1948 house in Denver and noticed my galvanized pipe is starting to rust. Do you think I should be concerned and have the piping replaced? Thanks.

If you can see rust on the exterior, chances are that the interior of the pipes are not doing well either. Before something breaks and forces your hand, get some comprehensive estimates for repiping your house so that you can compare apples to apples, and check into the work history of the company. Doing so is simply being a smart consumer; sometimes great plumbers can have a lower than normal bid for a job if they are simply looking for jobs to help through a slow time. Make sure that they include what is being done (are they opening up the walls, or drilling through the floors of cabinets to run water to vanities and the kitchen sink). If there will be drywall repairs required, do they calculate the repairs and use a subcontractor, or is it your responsibility. Will they be insulating all the water lines when reinstalling them? Do you want a recirculation system installed at the same time? There are a lot of things that are optional, some are luxuries, some help save a lot of energy(insulation). Decide what you want before getting bids so that there isn't any question of what you expect, and get a bid in writing. Most legitimate companies will require a downpayment on a job of that size, typically half of the estimate.

a little surface rust at a couple of locations is nothing to worry about.
joints where the galvanized meets brass are always a concern.
in either case, i have never seen galvanized pipes simply explode from inside and cause great flooding. left undisturbed they simple clog and greatly reduce water flow.
so if you don't see any leaks or stalactites growing on the piping, don't worry

It depends on what you mean by "rust".

If you have genuine concerns, you can drain the system and break a union. Inspect both sides. Best Wishes