There should always be a limit  - what are you doing to reset the default? FYI,
there is a pretty good reason for the 50 MB limit, doing anything larger
requires pretty hefty amounts of RAM. You'll need 2x the size of the uploaded
file of free memory on each farm server touched in the process (e.g. web front
end and SQL) to successfully  complete the upload  based on the way uploads are
buffered when writing to SQL server.

That is a "server setting" which you can adjust:
- Goto "SPS Central Administration".
- Select "Configure Vitual Server Setting from the virtual Server List page" in
the "Portal Site and Virtual Server Configuration" section.
- Select your server from the list.
- Select "Virtual Server general settings" from the "Virtual Server Management"
section.

From this page  you can change the "Maximum Upload Size".

I went into the SharePoint Central Administration page  and removed the
default limit  for the maximum upload  file. The field is currently blank.
Should I have a value in that field, i.e., 75MB?

So what you are saying below is that if I want to upload a 50MB file, I
need at least 100MB of free memory in order for it to work. Currently I
only have one server that does everything (web server, indexing,
searching). I don't have a server farm where I designate each server to
perform different task.

Yes, you need to set a value there. And yes, you'll need at least 100 MB of
memory free on your single server config to upload  a 50 MB file.

I tried uploading  a 30MB file  and I get the same results. I went into the
SharePoint Central Administration page  and put in 75MB for the limit. I verified
that I have at least 100MB of free memory.

Have you been successful doing this in both the normal  uploading way and also
using the Explorer view  by cutting and pasting the document? I'm running out of
ideas.

Yes, I have done uploads of this size on many occasions. Are you sure you have
at least 100 MB of physical memory free? Swap space is not enough, you need
real RAM. Also, what speed of connection do you have? It might be that the
upload is timing out if you are trying to do this over too slow of a connection.

I need to do some more testing. After sending out that email yesterday, I went
back and tested the 30MB file  and it worked and I verified that I had 145 MB of
free memory. But when I ran it earlier in the day with the same file, I noticed
it failed when I had 101 MB of free memory. I will try to increase the file size
by 5MB each and see what happens. What was the largest file size that you were
able to successfully  upload?