Question: Did Peter Parker take part in, or have knowledge of what happened to the rest of the radioactive spiders? Were they disposed of or are they are still hanging around in a lab somewhere?

Answer: 
I'm not sure whether this was retconned (and how many times...), so I'm going by what was shown on Spidey's first appearance, on Amazing Fantasy #15.

According to that, there were no other radioactive spiders. One single spider was accidentally irradiated, and it has bitten Peter Parker:

![Radioactive spider biting Peter Parker](https://i.stack.imgur.com/xhKad.jpg)

Apparently, spiders were insects in 1962

The spider was dying due to the amount of radiation it absorbed, so we can assume its body was disposed (by the janitor?).
**Amazing Spider-Man** (Cinematic Universe)
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*When the question indicated spiders (plural), my assumption was the recent Amazing Spider-Man movie which featured dozens of transgenic spiders weaving for Norman Osborn. In most versions of the canon story, there was only one spider, which was irradiated.*

As far as I can tell, the spiders are still at Osborn's laboratory being used for whatever insidious and yet financially profitable scheme they were commissioned for. In this particular instance, I don't believe they were strictly radioactive, let's call them [transgenic](http://en.wikipedia.org/wiki/Transgene) spiders.

Their bite, while painful, does not appear to offer superhuman abilities to anyone besides's Peter Parker indicating, perhaps a greater purpose or genetically engineered process being held within or released through the bite of the spider.

Though it was not clearly stated the radioactive spiders would not have had the same effect on anyone else that they had on Peter. It was meant to be revealed during the course of the movie that Parker's powers were not an accident as they appeared but something done intentionally.

To cover the whole conspiracy theory properly, you need to see: [Was the Untold Story Cut from the Amazing Spider-Man?](http://badassdigest.com/2012/07/05/was-the-untold-story-cut-from-the-amazing-spider-man/)

**Amazing Spider-Man** (Marvel Earth-616)
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If you are talking about the Marvel Earth-616, there were no known "other spiders" after the first one bit Peter Parker. It died from radiation poisoning soon after spreading its radiation-activated powers to an unwitting recipient.