Are the Windows updates necessary? Do they cause the computer to run slower? The updates are automatic, but I question if they're helping or hurting. Please advise.

Even I have constant updates!
It will only do good to your computer!

Yes, you do need them as they fix security flaws within your system and often provide greater performance upgrades. If you are worried about them slowing down your computer have them download and install at a time when you aren't using your computer, i.e sleeping.

Automatic Updates are a real pain (for Windows Vista), what I do is disable them:

Start>Control Panel>Windows Update>Change Settings>Never Check For Updates>Uncheck All Options>Ok

Then go on the Microsoft website and look up Service Pack 1,2,3... download them and install them.
Note: In order to install, for example SP3 you need to have SP1 and SP2 already installed.

Doing this shortens the pain of installing and configuring updates for Windows one by one, Which sometimes can take up to a half an hour. Service Packs are basically a whole bunch of updates that are in one pack.

Service Packs do help allot, here is an example:
When I first got my laptop I installed Battlefield 2 (awesome fps game) and it played good for a couple of days and than started to lag like , I'm talking like 2 frames per second here, brutally slow! So I downgraded to Windows XP, and installed BF2 no lag at all. Soon I realized I was missing almost have of all the drivers I needed so I went up to Vista again. I installed BF2 on Vista again this time with SP1 and there was no lag at all. SP1 alone increased the speed of the start up and decreased the amount of CPU Vista uses.

So as you can see windows updates do help, but I like to install them in packs.
My answer to your question is that you should install updates they add security updates and make your computer run faster.