the grand jury system
There's a reason why the grand jury system is enshrined in the US constitution - specifically in the Fifth Amendment, part of the Bill of Rights. As Gareth wrote, it has its origins in English Common Law (specifically in Henry II's transfer of power to royal courts and in Magna Carta); but its deployment in the US had a somewhat different purpose.
In principle, grand juries offer an important check on prosecutorial power. That's why they have investigatory powers - so that the members of the grand jury can determine whether prosecution is legitimate, or a case of overreach, political oppression, personal vendetta, subornation, etc.
Unfortunately, in practice, statistics show that grand juries are incredibly unwilling to refuse to indict. In 2010, Federal grand juries returned an indictment in 99.99% of cases. It's just one of many problems with the US prosecution system today; other major ones include the two types of "chickenshit prosecutions", the trend for the various state's-attorney offices to serve as stepping stones to other political positions; and extremely excessive sentencing laws passed by cowardly legislators who don't want to be seen as "soft on crime".
The idea of a grand jury system remains a good one, though. Other countries which have dispensed with them aren't necessarily paragons of judicial virtue.