We present optical, X-ray, high-energy ( ##IMG## [http://ej.iop.org/icons/Entities/lap.gif] lap 30 GeV) and very high energy ( ##IMG## [http://ej.iop.org/icons/Entities/gap.gif] gap 100 GeV; VHE) observations of the high-frequency peaked blazar Mrk 421 taken between 2008 May 24 and June 23. A high-energy γ-ray signal was detected by AGILE with ##IMG## [http://ej.iop.org/images/1538-4357/691/1/L13/apjl295580ieqn1.gif] $\sqrtTS=4.5$ between June 9 and 15, with F ( E >100 MeV)=42 +14 –12 × 10 –8 photons cm –2 s –1 . This flaring state is brighter than the average flux observed by EGRET by a factor of ~3, but still consistent with the highest EGRET flux. In hard X-rays (20-60 keV) SuperAGILE resolved a five-day flare (June 9-15) peaking at ~55 mCrab. SuperAGILE, RXTE /ASM and Swift /BAT data show a correlated flaring structure between soft and hard X-rays. Hints of the same flaring behavior are also detected in the simultaneous optical data provided by the GASP-WEBT. A Swift /XRT observation near the flaring maximum revealed the highest 2-10 keV flux ever observed from this source, of 2.6 × 10 –9 erg cm –2 s –1 (i.e. >100 mCrab). A peak synchrotron energy of ~3 keV was derived, higher than typical values of ~0.5-1 keV. VHE observations with MAGIC and VERITAS between June 6 and 8 showed the flux peaking in a bright state, well correlated with the X-rays. This extraordinary set of simultaneous data, covering a 12-decade spectral range, allowed for a deep analysis of the spectral energy distribution as well as of correlated light curves. The γ-ray flare can be interpreted within the framework of the synchrotron self-Compton model in terms of a rapid acceleration of leptons in the jet.