I'm looking to intall a new power supply on my HP computer, something around 500W. Can any power supply be installed on any computer or are there differences like in graphics cards and stuff like PCI-E and APX?500W is quite a bit of power?  Why do you think you need that much?  Tell us about your system.

"Can any power supply be installed on any computer ...?"   No, you generally need to match the form factor of the power with the case and motherboard.  In other words, if you have a mid-tower case with an ATX motherboard, you should get an ATX power supply.  And, yes, the features of your motherboard, such as PCI Express vs. OLDER AGP and SATA hard drives vs. older IDE/PATA hard drives must also be taken into consideration.  

If you motherboard preceded PCI Express, you probably have a 20-PIN connector on the motherboard for the power cord from the power supply.  But, if you have newer motherboard with PCI Express, you'll have a 24-pin power connector on the motherboard.
  
So, clearly, there are differences in computer cases and motherboards and power supplies and you must select one that matches your hardware.  Also keep in mind that some major brand computers do not CONFORM to industry-standards, such as the ATX form factor, in their case design; this means you may need to get a "proprietary" power supply to match their proprietary design.  

If you can tell us the exact model of your computer, maybe someone can give more specific advice.
And some manufacturer's use proprietary power supplies with unusual connectors.Thanks for your replies very helpful.  The system is actually a HP Pavilion a562n. The reason for a new power supply is to run a more powerful graphics card I installed and my current power supply is only 250W and it requires at least 450W. As for my motherboard I know very little about motherboards the connections are definiately not PCI-E however.HP and Compaq Desktop PCs -  Motherboard Specifications, P4SD-LA (Oxford) states that you have an AGP slot.  So, do not get a PCI Express card; you can not use it.

What card did you get or intend to get?  450W is a rather high requirment.  What is your objective in this upgrade?  A good gaming machine?  

If gaming is not the objective and you're just seeking better performance for general use, I'll  suggest something like this:  eVGA 256-A8-N313-LX GeForce FX5500 256MB 128-bit DDR AGP 8X Video Card - Retail
 Note that the statement power requirement for this card is 250W minimum.  So, you could feel confident in buying it.The graphics card I installed is a nVidia GeForce 7300 GT.  I really enjoy playing BF2 so I wanted a card that would run the game at the highest graphics levels. Currently even without running full power it is more than capable but everytime the machine starts it provides a warning and notice that the card is running at less than required power and will cut its performance. I appreciate your help and the information you have provided so far.Some of the major brand computers have proprietary power supplies, meaning they do differ from the industry-standard ATX specifications.  I do not know what the situation is concerning your particular model computer.  However, careful inspection should provide some solid info.  Does your motherboard have a standard 20 pin or 24 pin connector for the power cord from the power supply?  Page 32 of this Power Supply Design Guide shows dimensions of an ATX power supply.  Besides the outer dimensions, you should also be aware of the spacing of threaded mounting holes; do they match the holes in the back of your computer case?  

If you have a local retail seller of computer components, taking your power supply into the store and ASKING for confirmation from a sales person that they a power supply they sell will fit your computer might be wise.