Having said that, I understand that all sorts of activities can be prevented from happening (like the appointment of judges) simply by a single member of Congress threatening to filibuster it to pieces. Is that so? And is there any reason why Congress members haven't done anything to change this system (apart from each side wanting to have that shot in their locker for when they're in the minority)?
The Senate has an open ended debate policy while the House has a time limited debate, with the time set by the Speaker. Debate in the Senate can be ended by a parliamentary motion, cloture, that requires a super majority of members. The Senate changes the speaking rules from time to time, to give more or less power to filibusters.
From recollection it is something like this.
At one time, it was required for one speaker to stay at the lectern. The senator could stop speaking while a question was being asked but had to stand there the whole time. This pretty much limited the filibuster. Some years back the rule was changed to allow the speech to stop for the night, that is when it became a more powerful tool. The cloture vote requires a 2/3 super majority. So pretty much any law had to have 2/3rds of the Senate to pass.
I remember watching a debate on a Republican, newly in the majority, proposal changing the cloture requirement to 50%. Democrats, now the minority party, were "frothing" over this proclaiming the Republicans were trying to stifle the rights of the minority, or similar. While before the change of control the majority Democrats had proposed various similar changes and were met with Republican froth.
The rules have changed somewhat since then and I am not sure what they are are now. But in general one Senator cannot exclusively by himself indefinitely hold up legislation or nominations. It can only be done with support of his party. But for high ranking Senators, the party will generally not go against them for nominations approvals.
I've always felt the Senate should be time limited on how long it can hold up an appointment. The Senate makes its own rules, only a constitutional amendment can change the way things work.