Yes, you can, within reason. You probably can’t activate that old flip phone, but if you have a phone in a drawer made in the last ten years, it should at least work for calls on the network it was designed for. You probably won’t get much by way of internet, but let’s be honest, you didn’t get much by way of internet with that old phone when you used it.
If you think you’re going to use a phone in the future, it’s worth getting it “unlocked.” Unlocking involves changing the phone’s software so it could work with any network that its chips and radios can support. This will open up a lot of options. Generally there is a small fee to do this and some cell phone repair places will do it.
Even if a phone is not unlocked, you can generally reactivate it easily. With AT&T and other carriers that use SIM cards, it’s really just a matter of a new card. With Verizon and carriers that don’t need SIM cards, it’s a little more complex but not much.
So, keep that old phone or sell it to someone else who wants it… it’s still going to be good.