Non-standard LEGO themes
There are huge number of different LEGO set themes these days. A lot more than the original three introduces back in 1978 (city/town, castle and space). Most of those themes use (mostly) standard LEGO bricks, but there are few that have their own distinctive pieces.
The most well known such themes are Dublo- and Technic sets. Former featuring big, double sized bricks and later using pins instead of studs for primary connectors between bricks.
Bionicle might also fall into this category of well known themes that doesn't use standard bricks, but mostly technics style connections with a distinctive pieces. There are also few other themes that use similar building techniques as Bionicle.
Apart from few unique themes, like clickits, the rest of the "special" themes mostly use standard bricks. But they are distinctive from the regular themes by a few factors. Some of them use different kind of minifigs, like the old Fabuland sets or the towards girls targeted sets like Bellville or Friends. Some of those sets also use a different colour palette, offering bricks in colours not available in any other themes.