What could be the culprit behind a rattling inside HVAC unit?

The HVAC system in my house in San Antonio has the compressor unit outside and the air handling unit inside (located in a utility closet shared with the water heater). The unit shakes while the blower is on - lots of metal rattling sounds. It does blow cold air - the house is quite comfy, but it seems pretty loud... and louder than it has been in previous years. We've been in the house since 2001. My attempts to address this have been unsuccessful. I've kept the filters pristine, tightened all of the bolts on the metal housing and cleaned (as best I could) the fins on the squirrel cage.

Any ideas about what's causing the rattling noise, or is this just normal?

The blower wheel is out-of-balance for some reason. Dirt build-up in the vanes is the most likely culprit, although it could also be a faulty wheel, missing/ejected counterweight, or some other object/debris in the wheel. The most effective way to clean the wheel is to remove it completely from the motor/housing assembly and thoroughly spray it out with water. If you elect to try it yourself, pay attention during disassembly to assure a successful re-assembly.

Just out of curiosity, I took the top cover off while the blower was on. I know that's a bad idea... but it was only for a few seconds. The rattling stopped.

Does that change your assessment at all?

I very much appreciate the input.

EDIT:

Actually it's still there. I'd just been putting pressure on the metal enclosure when I took the top cover off... when I tried it just now, it's rattling pretty good. Your initial answer sounds very likely after further inspection. I think I'm about a month (depending on weather) from failure on this blower unit... cleaning isn't going to fix it.