Launched on 2 June 2003, the probe went into orbit around the Red Planet in the December of that year.
Its most significant discovery is probably the detection of water-altered minerals at the surface.
A sample of these, clay minerals, were recently drilled and analysed for the first time by the Americans' latest rover, Curiosity.
MEx retains a full suite of working instruments and has sufficient fuel to keep operating deep into this decade, although hardware failure in the harsh environment of space is an ever-present threat.
Two years ago, engineers were challenged to find a new way to operate the satellite when it developed a serious memory glitch.
"It was our first mission to Mars. We actually planned for a two-year lifetime at the planet with a possible extension of another two years; and now here we are at 10 years and counting," said Alvaro Gimenez, Esa's science director.
"It's been a great success from an engineering point of view, but also from a science perspective because of the extraordinary global view it has given us of Mars," he told BBC News.
MEx's seven instruments allow it to study the atmosphere, the surface and sub-surface of the planet.
Its German-led camera system has imaged over 95% of Mars, with two-thirds mapped at a resolution of 20m per pixel or better. Much of this has been done in stereo, which has allowed scientists to build remarkable 3D views of the surface.
Key observations have included the detection of methane in Martian air, a potential signature of biology; and the identification of vast landforms cut by glacier activity in the distant past.
MEx has also seen evidence of relatively recent, geologically speaking, volcanic activity; and it has probed the polar caps with its radar to determine the presence of huge deposits of water ice.
At the south pole alone, there is enough water locked up in ice to cover the entire planet with a layer of liquid 11m deep.
But it is the mapping of clays and other hydrated minerals that is most frequently cited by Mars researchers as the probe's major contribution to their field of study.
Esa released new maps from MEx on Monday that detail not only the location of the clays, or phyllosilicates as they are often called, but other mineral types as well, including pyroxene, olivine, haematite (iron), and the weathered materials - the ubiquitous dust - that give Mars its red hue.
The information contained in these maps has allowed MEx scientists to construct a probable history for the planet.
This describes a very early wet phase when water was stable at the surface followed by a drying out as the Martian climate abruptly changed about four billion years ago.
It provides a guide to where Europe should send its 2018 ExoMars rover, says Prof Jean-Pierre Bibring, the principal investigator on MEx's Omega instrument.
"[The maps] give the prediction of where on Mars to find the relics that might have been habitable," he told a 10th anniversary MEx conference in Darmstadt, Germany.
"If life started elsewhere than on Earth, we know where to go to. We know the places; they have been identified. We have got to go to the Phyllosian, and ExoMars should do that."
The "Phyllosian" is the period in Mars history, some 4.2-4.5 billion years ago, when the clay beds seen by MEx are thought to have been formed.
Mars Express has some spectacular observations planned in the months ahead.
In December, it will attempt an extremely close flyby of the planet's moon Phobos, skimming 47km from the surface. And then in early 2014, it will turn its instruments on Comet C/2013 A1 (Siding Spring), which is passing within just a few hundred thousand km of the Red Planet.
The one major blemish on this European venture to Mars remains the loss of the Beagle2 lander.
The small British-built surface probe was carried to the planet by MEx and released just a few days before the scheduled touch-down.  A picture of the disc-shaped Beagle2 disappearing into the distance is the last contact Esa had with the lander.
Jonathan.Amos-INTERNET@bbc.co.uk and follow me on Twitter: @BBCAmos
The European Space Agency (Esa) is celebrating the 10th anniversary of its Mars Express mission.