Does it take longer to download a zipped file than an unzipped file?

When the connection is using compression, then of course.

You cannot efficiently compress data 2 times. So when compression is turned on, a 1 MB zip file will be transferred slower then a 1 MB txt file.

NB: This is dependent on the transfer protocol. FTP or other protocols don't have built-in compression. HTTP has.

It's not true if you are downloading via standard FTP or HTTP. For other connection types see Christopher's answer.

Assuming the same connection the speed of download is determined by the size of the file.

There might be a delay at the end of the download if you have automatic virus checking enabled as it will have to open and unpack the zip file to check the contents rather than being able to check the file directly.

you must notice it's has no difference in HTTP protocol because in server and in router they use GZIP to zip packet and then send therefor if you zip or non they act the same.

As already mentioned, HTTP traffic can be compressed, but it isn't always.

You may have read this at a time when people used phone modems instead of adsl/cable modems. In this situation, the text was compressed before sending or receiving, so your text file would have been sent faster.