How can I tell if my server is serving GZipped content?

See in the response headers. In FireFox you may check with Firebug.

Content-Encoding    gzip

If server supports gzip content then this should be displayed.

In new version of chrome, Developer tools > network, you can right click on Column name, and select content-encoding option and add that column (black box in image).

and if you want to see the size of that gzip content, as @Outfast Source - than you can click on icon which is next to View (displayed as Green box in image).

so you can see which content is gzip enabled.

It looks like one possible answer is, unsurprisingly, curl:

$ curl http://example.com/ --silent --write-out "%{size_download}\n" --output /dev/null
31032
$ curl http://example.com/ --silent -H "Accept-Encoding: gzip,deflate" --write-out "%{size_download}\n" --output /dev/null
2553

In the second case the client tells the server that it supports content encoding and you can see that the response was indeed shorter, compressed.

Update

Chrome changed the way it reports (see original answer if interested). You can tell using Developer Tools (F12). Go to the Network tab, select the file you want to examine and then look at the Headers tab on the right. If you are gzipped, then you will see that in the Content-Encoding.

In this example, slider.jpg is indeed being gzipped.

Compare that to this very page that you are on and look at a png file, you will see no such designation.

Just to be clear, it isn't because one is a jpg and one is a png. It is because one is gzipped and the other one isn't.

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Previous Answer

In Chrome, if you pull up the Developer Tools and go to the Network tab, then it will show the following if there is no compression:

And the following if there IS compression:

In other words, the same number, top and bottom, means no compression.