Typically it depends on the shifters. Here's a basic breakdown...
- Friction Thumbshifter - multiple shifts in both directions are possible but you have to "know how to shift" meaning you need to feel yourself into the gears
- Indexed Thumbshifter - multiple shifts in both directions are possible and each gear will click into place
- GripShifters/Twistshifters - same as Indexed Thumbshifters
- 1st and 2nd Generation RapidFire Shifter and Dual-Control - multiple shifts (usually a limit of 3) in the direction of pull are possible (upshifting chainrings or downshifting cassette for high-normal; upshifting chainrings or upshifting cassette for low-normal) but only a single shift is possible in the cable-release direction (downshifting chainrings or upshifting cassette for high-normal; downshifting chainrings or downshifting cassette for low-normal)
- 3rd Generation RapidFire Shifter (Dual-Release) - multiple shifts in either direction are possible (usually a limit of three in the pull direction and two in the release direction - shifting direction as per hi/lo-normal biasing)
And as others have said, double-shifting (shifting front and rear simultaneously) is supported but not often recommended... especially under heavy offroad jouncing.