Running

Yes, you can. Many people do at our age.

Google coolrunnings C25k. There is a great program,

I ran my first 5K at 52; 5 years later I'm running half-marathons & am a wannabe triathlete.

Is there a running specialty store in your town? Many of them offer "learn to run" programs free of charge and can make sure you've got the right shoes (it's worthwhile getting your gait analyzed - the right footwear can make a huge difference, don't rush off to a big box store - most of their staff are not runners and are not trained to look after your needs properly)

Depending on how out of shape you are (when I started running I couldn't even get around the block) you may want to start with walking. When you feel ready add in 1 minute of gentle (slow) running followed by several minutes walking, rinse & repeat. Every week or two (you be the judge of your own progress) add a minute to your running intervals - again keep it slow - until you can run continuously for 10 minutes. At that point you may either keep going with 10 minutes running followed by 1 minute walking (a method promoted by Jeff Galloway and used by a great many recreational runners) or you may want to increase your continuous running times - either way build up gradually. The leading cause of running injuries is trying to do too much, too soon, too fast.

Run every second day to give your body time to recover and adapt; there are a lot of physiological changes brought about by running - all of the good - but they take time.

On non-running days you should still be active (walking,biking, swimming, strength training) and you should take a full recovery day weekly (do something low impact, low intensity). Strength training is a great way to address muscular imbalances and improve injury resistance (and contrary to what you may have heard weight lifting does not cause women to become bulky unless you're taking steroids and spending 8 hrs a day in the gym, the same is true for most men too....)

Check out runnersworld.com for lots of free tips on running, strength & core exercises (there's a column called the Newbie Chronicles - it should be mandatory for every new runner, good information and funny)

have fun!