  [Abridged] Context. To construct and interpret the spectral energy
distribution (SED) of BL Lacertae objects, simultaneous broad-band observations
are mandatory. Aims. We present the results of a dedicated multi-wavelength
study of the high-frequency peaked BL Lacertae (HBL) object and known TeV
emitter 1ES 2344+514 by means of a pre-organised campaign. Methods. The
observations were conducted during simultaneous visibility windows of MAGIC and
AGILE in late 2008. The measurements were complemented by Mets\"ahovi,
RATAN-600, KVA+Tuorla, Swift and VLBA pointings. Additional coverage was
provided by the ongoing long-term F-GAMMA and MOJAVE programs, the OVRO 40-m
and CrAO telescopes as well as the Fermi satellite. The obtained SEDs are
modelled using a one-zone as well as a self-consistent two-zone synchrotron
self-Compton model. Results. 1ES 2344+514 was found at very low flux states in
both X-rays and very high energy gamma rays. Variability was detected in the
low frequency radio and X-ray bands only, where for the latter a small flare
was observed. The X-ray flare was possibly caused by shock acceleration
characterised by similar cooling and acceleration time scales. MOJAVE VLBA
monitoring reveals a static jet whose components are stable over time scales of
eleven years, contrary to previous findings. There appears to be no significant
correlation between the 15 GHz and R-band monitoring light curves. The
observations presented here constitute the first multi-wavelength campaign on
1ES 2344+514 from radio to VHE energies and one of the few simultaneous SEDs
during low activity states. The quasi-simultaneous Fermi-LAT data poses some
challenges for SED modelling, but in general the SEDs are described well by
both applied models. The resulting parameters are typical for TeV emitting
HBLs. Consequently it remains unclear whether a so-called quiescent state was
found in this campaign.
