Updates won't install

I'm pretty lazy about my updates, and tend to put them off for awhile, but now that I have 12 waiting to be installed I finally decided to do it. The problem is, they won't install. I click on the apple, click "software update...," it searches for new software, finds my 12 downloaded items, and says "you must restart your computer to install." So I do (by clicking on the "install and restart now" button). But then they're still there, still waiting to install. I've done this several times in the past 2 weeks to see if it was just being stupid, but they're definitely not installing. I came on here and looked around but couldn't find a solution; some people say select "download only" and install them manually, but I can't find the "download only" option. I did manage to find the "installed software" area in system preferences, and discovered my most recent software was installed of October 2011. I'm lazy about software updates, but I know I've (tried to) install stuff since then, so apparently this problem has gone on for awhile. Help please? I really need some of this new software. :/
If this means anything, sometimes it tells me I have 8 items to install, and sometimes it tells me I have 12. It seems to alternate. But even when it says I only have 8, those other 4 haven't been installed.

I have a 13 inch macbook with OS 10.6.8 on it (snow leopard). It's almost 3 years old.
The software that's not installing includes: remote desktop client update, security update, safari, itunes, airport utility, Java, apple software installer update, superdrive firmware update...

Why anyone would be "lazy" about installing updates from Apple is beyond me. I can understand Windows users doing this, but you own a Mac not a Windows machine.

Try installing them one at a time. In other words, only accept one at a time to see if it will install. If not, then you have other troubles. It may be time to reinstall Snow Leopard and start over.

I've used windows my whole life till this mac. Old habits die hard.

I tried that though, and it worked! Whoo hoo. :] Except it didn't work for 2 items - safari and security update 2012-004. They both have this little gray and white arrow to the left of them, pointing to the left. Nothing happens when I click on it. Any ideas about why those two are different?