I know you're wondering what time it is on Mars right now. Here, let me check for you... It's, uh, yeah okay I give up. Mars time is tricky, because it's similar to Earth time but not quite the same, and the difference is enough to drive the people working on Mars missions a little bit nuts.
One day on Mars lasts about 24 hours and 39 minutes, and every Mars mission (including Opportunity and Curiosity) runs on this "local time" schedule. For all the Earthlings involved, this means that their day starts 39 minutes later every day. This causes all sorts of problems, the first of which is that using the word "day" gets ambiguous, so Martian days are now called "sols," short for "solar days," giving us yestersols, tosols and nextersols.
Anyway, let's get back on Mars time.
In 2004, when Spirit and Opportunity were on their way to Mars, the Jet Propulsion Laboratory asked a local watchmaker to come up with some timepieces that would run on Mars time instead of Earth time to help the agency keep up with its distant rovers. It's easy to do this sort of thing with a computer, of course, but not with a quartz or mechanical watch without a complete redesign. The watchmaker spent two months on the project, and came up with a way to add tiny lead weights to the guts of mechanical watches to get them to run just slow enough to sync up with Mars time. All the rover team members got one of these, and you can too, in preparation for your first trip to Mars.
And as for what we might actually start doing when people are living on Mars, nobody's quite sure. In his excellent Mars trilogy, science fiction author Kim Stanley Robinson suggests a "timeslip," where Mars clocks keep standard 24 hour Earth time but freeze for 39 minutes between midnight and 12:01 am. Other options include stretching out seconds by a small fraction such that 24 Mars hours make one Mars day, or just dumping the whole base-60 system (a carry-over from the Babylonians) and going with a brand new base-10 metric clock for Mars instead.