I have an old Dell Insprion 9300 which I am growing to hate. It is running Windows XP. I got it in 2005. Its fan is always running. Is that normal?
Wrong, there’s lots of reasons why excess heat is generated, saying it’s down to how many programs you have open is incorrect. If you have programs running idly in the background for example it’ll use no extra cycles and thereby generate no excess stress. 
it depends on programs if you running more programs then it will run very fast and generate heat but if you are using a single or two programs then its running not so fast if you have some problem regarding fan then you should go to nearest laptop repair shop and repair your fan
:x Uggh well, sometimes it works all the time other times it goes on and off.
It probably just turns off when the machine is cool enough not to need the extra burst of airflow. It’s very common for fans to work 24/7 though.
Another Designer… so you want to know if it’s normal for the mechanism which prevents your machine from overheating to continuously do it’s job? 
I’d be worried if it stopped and couldn’t run… It depends on the machine’s design and which fan you are talking about. It doesn’t take much to heat up a PC when it is running a few programs, and needs a good airflow. Some fans are setup to run at different speeds depending on “load”.
As it is a Laptop in your case; it will have restricted airflow and heat faster than a Desktop so typically the fan will constantly run.
Ventilation duct must be chocked. Use compress air can to clean the duct.