A cage is a cage is a cage.. right?
A parrot's cage is more than just a place to park your bird while you cant be with him. It's a home, a nest, a roost, and a playground. You, as the human companion, are responsible for making sure not only that the cage is appropriately sized, but also for making sure that everything in it is as right for your parrot as possible.
Lets take a Congo African Grey for example. Appropriate cage sizes can run from as small as 30"x30"x30" up to a room of their own. I recommend a larger cage for a Grey, simply because your going to need to put lots of intelligent and stimulating toys in there to keep your buddy busy while your not there to be his entertainment.
Take a minute when looking at cages to look at yourself. Is this cage going to be taller than you are? How about the bird when he's on top of the cage? A bird who stands taller than you can feel dominant, and act accordingly. Be sure your head will be higher than your parrots! Also, how do you feed and water the parrot with that cage? The best cages will have food doors that allow you to do this from the outside of the cage. You'll disturb the bird less that way, and its safer for a babysitter, or other stand in to feed your parrot should you have to go away for any extended period.
It is also important to consider the material your cage is made in. Most commonly you will get a choice between powder coated metal and stainless steel. There are good arguments for either, and it really boils down to a matter of personal preference. Powder coat can become chipped in time and need to be redone, however it is easy to clean and less expensive to purchase. Stainless steel tends to be stronger, which is important for big birds (such as macaws), but it tends to show fingerprints or other marks easily so the cage can often look dirty even when its not. When buying a small cage the price difference may be the deciding factor, but remember, stainless steel lasts a long time, so consider the costs of replacement powder coat before making your choice.
You need to be sure that not only is the size appropriate for the bird you are housing, but the bar spacing works well too. You don't want your Ringneck sticking its head between the bars and injuring itself, or even killing itself. Each different bird has different needs for cage size and bar spacing, read up and learn before creating your parrot's new home. If your budget won't allow you to get a large cage, then don't get a large bird! Also, take a moment to consider the bars on your parrot's new cage, do they run both vertical and horizontal? They should, to provide lots of fun climbing! The last thing to look at before purchasing that new expensive cage? The door. A bigger door makes it much easier to get your parrot in and out of its cage.