Shared hobbies and interests are good - so are separate ones. Spending ALL off of your time together is smothering, though, and is one of the best ways to chase the spark right out of things for most couples. It's hard to find much to talk about when you're together constantly! (And, really, how interesting is it to just talk about work stuff?)
Even if you don't have any hobbies/interests you don't share, you don't always have to participate in the same events.
For instance, my partner and I both enjoy roleplaying games (RPGs). We don't have to play in all the same games. He runs games for groups in which I don't play, and I'm free to play in games run by other people or to run games myself.
Couples involved in the SCA often join different guilds, which have different practice/meeting schedules. Musicians can play together as well as in different ensembles and in solo gigs.
Still, I think it's healthy for people to try to develop some hobbies/interests that are separate. I do needlework. Sam plays video games. He's never going to pick up a needle, and I can't understand what anyone gets out of those games. We support each other's separate habits and find our time apart well-spent - even when we're in the same room doing separate things, it's not the same as doing the same thing together. We have new things to talk to each other about when we go off and pursue our interests separately.
If you have children, especially older ones, it's nice if one of you shares a passion with one of them that can be the basis for special time together. Or, each of you may want to use pursuit of a hobby to get some precious child-free time. Just make sure things work out fairly if that's the case, so you both get time to do that. Rock-hounding can be great fun for kids, though, and teens can be very helpful with researching your family tree. Even young children can enjoy gardening.
When you come back together after spending time apart, you'll feel refreshed and have more energy for each other.