There is a crowd-sourcing initiative to look for aircraft debris in commercial satellite imagery; the Chinese thought one of their reconnaissance satellites had photographed such debris on March 9 (but it turned out to be unrelated); and US authorities said there were no signs of an explosion in data from US infrared Early Warning satellites.
Let us look at the latter two cases. What satellites were used to look for an explosion and for debris?
SBIRS: looking for a mid-air explosion
First, the reported non-observation of a mid-air explosion by US military infra-red Early Warning satellites. Two such systems exist: the older DSP (Defense Support Program) and the newer SBIRS (Space-Based Infrared System).
Both US systems are dedicated to detect ICBM launches and have a semi-global coverage. They use infrared telescope equiped satellites to look for the infrared signatures of rocket launches. They also detect other transient infrared events such as meteoric fireballs, re-entering spacecraft, surface detonations and, it is claimed, exploding aircraft.
According to the news reports, the SBIRS network was used to look for any traces of a mid-air explosion of flight MH370. Defense specialists quoted in the news article claim that the SBIRS system is capable to detect such mid-air aircraft explosions.
SBIRS currently consists of four satellites (see image above): two satellites in Geostationary orbit (SBIRS Geo 1 and SBIRS Geo 2, 2011-019A and 2013-011A), and two satellites in a Highly Elliptical Orbit (USA 184 and USA 200, 2006-027A and 2008-010A) with a SBIRS package piggybacked on to them.
Of these, two satellites had a view of the area where flight MH370 disappeared at that moment it disappeared: the geostationary SBIRS Geo 1 and the SBIRS HEO USA 200:
It is less likely that the older DSP system was used. It probably does not have enough sensitivity, and the spokespersons in the news articles explicitly talk about the newer SBIRS. Two DSP satellites, DSP F21 and DSP F22 (both in a geostationary orbit) would have had a view of the relevant area:
Gaofen 1: Chinese satellites looking for debris
On March 12 a Chinese government website released military reconnaissance satellite images of possible aircraft debris floating near 105.63 E, 6.7 N. The images were reportedly taken on March 9 near 11 am (presumably Beijing time). They later turned out to be unrelated to the missing aircraft (or rather: they have not been found by searching ships).
China orbits several optical reconnaissance satellites, in the Yaogan and Gaofen series. According to analyst Brian Weeden, the images were likely taken by Gaofen 1 (2013-018A), as this satellite reportedly has enough resolution.
The listed time of "March 9, 11 am" corresponds to 9 March 3 UT. Gaofen 1 made a pass over the area at 3:40 UT, almost right overhead.
The only other two Chinese imaging satellites passing near the area around that time are Yaogan 12 (2011-066B) and Yaogan 19 (2013-065A) who passed near 2:45 and 2:50 UT, but more to the East (but with the target area nevertheless in their visibility footprint):
Note added 18/03/2014: there is a follow-up post here about the Inmarsat 3-F1 detection of ACARS ping-backs from the aircraft, and the potential use of SIGINT satellites.