I agree with the rest of the posts saying that a malware is not dangerous if quarantined and if it stays in the quarantine.
But I'd like to add a qualifier - this is only true if the software works as intended.
Antivirus software, just like any other software out there, especially software that has loads of code to parse untrusted data is bound to have bugs in it somewhere. There have been plenty of cases of security vulnerabilties in the antivirus software itself, sometimes even creating infection vectors where they would otherwise not exist.
This makes me wonder - at some level the malware has to be "neutralized" before quarantined, perhaps by doing something to the data of the virus. The LZO bug has told us that subtle faults in algorithms can exist for a long time and be widely deployed.
Let's imagine for a moment that the recently discovered LZO bug could be triggered by compresion rather than decompression. (Which is not the case. But who knows what bugs lurk?) And let's further imagine that a hypothetical antivirus product uses LZO to compress the malware as a step in containing it.
Let's further imagine an adversary creating a piece of malware that is detected as malware (easy enough to do, just include the EICAR string in it) and when quarantined causes remote code execution in the context of the antivirus process!
I'm sure you can imagine many variations on this theme.
So, short answer, yes, malware is harmless once quarantined.
Long answer, it is possible to imagine circumstances where a security bug in the quarantining process itself in the malware would cause a piece of malware to be able to infect your computer specifically through the quarantining feature. But I've never heard of this happening.