Hi,
well I think that the use of applets is shrinking but they can still perform some very usefull tasks. Look at the applet as a little program that you can send along with your webpage.Let's say this is a page where the user registers for something. Suppose you want to validate weather or not the user actually filled in characters in the first name field and not numbers for instance. Now let's say you don't use applets. The validation now takes place as follows...The user clicks "send" or something and then on the server (application or combined application/database server) the field validation takes place. It turns out the user accidently typed in the number 8 instead of an "i". Now a message has to be sent back with the request to fill something out anew and again the fieldvalidation has to be done.
Suppose however that with the registratioform you send a little applet along that maybe just checks weather the user types in actual characters. Without any datatraffic over the internet this can be checked right on the users computer. This saves time and datatraffic.
So applets have nice uses apart from the showing up as walking puppies on peoples homepages.
So why are they getting less popular? Well, you can't use
Java 2 really and Java 1 has it's limitations (as does Java 2 of course but the possibilities are more). Why not? Simply because the browsers you and I have don't use Java 2 Virtual Machines. So suppose you use Java 2 applets on your page then the first time a visitor of your page has to download a plugin from Sun which is about 4Mb or so. This is just once but it's an obstacle.
Servlets are getting used more these days, especially on corporate intranets. These you can few as applets running on an applicationserver where it also reduces the datatraffic and takes care of businessrules that can be checked before allowing any datatraffic to the database.
Applets are a very nice way to learn Java by the way because you don't have to worry about the frame/container for your applet. It's been taken care off for you.
Well,hope this helps a bit...

)
Patrick