Absolutely! Save 'em and plant 'em.
As has been said before, you could end up with some crosses so you might not want to make them the ONLY seeds you plant in case the results are not what you hoped for, but that's also part of the fun.
You can even save seeds from grocery store peppers, but again, results may vary.
I pull the seeds from the peppers, dry them a little on some paper towels and the pull off as much placenta as possible as soon as I can. Once they dry fully, I throw throw them in coin envelopes or ziploc bags... If using plastic, make sure they're fully dry. There are a bunch of threads discussing methods to harvest and store seeds.
Also, wear gloves with the hotter peppers... Even when you think the burning oils are gone, those things pack a mean punch.