While the physical part of changing the memory chip shouldn't be that hard (depending of ones soldering skills and equipment availability). I think the main question should be, Will the phones system architecture allow it to access/utilize the extra memory if it is added? Because if the answer to that question is no...there ain't much point in cracking the thing open.
Stoic is right. No. You can't. (Usually.)
First, the kind of chips you need aren't generally available. The kind of memory you need to look at is measured in Mb or Gb, and not in MB or GB. We're talking about individual chips and not banks of them.
But if you do have them, then you into different problems.
Parts of the firmware are compiled for specific memory.
Remember, different memory uses different voltages, with newer memory using less and less. So you'd also have power issues to worry about. You don't want to put 1.8 V through memory that needs 1.35 V.
However, it's a case-by-case basis and depends on your specific device. In general, no you can't.
However, if your phone has something like eMMC in it, then you can relatively easily. eMMC has a single point for the interface and insulates application designers from the specific memory type. This is the wave of the future for mobile memory and you'll see more and more of it. moviMMC and other stuff is coming as well, which will allow the same kinds of things.
In short, if you need to ask the question, don't even think about trying. Unless you have a phone to burn and don't care if you destroy it, then by all means, have some fun and experiment!