Great topic! My DH and I went through a year in our marriage where we realized we'd become disconnected, and needed to get some excitement going again. (this was before kids, we were just both quite involved in our work and drifted apart). Here are some things we did:
1. Took a massage class together. I would HIGHLY recommend this! It was terrific! Not only are you learning about good massage technique, and possibly learning about your partner's physical self in a new way, it feels great whether giving or receiving

We enjoyed it so much that we actually invested in an adjusting massage table (I am short, DH is tall). It is also something that can be done at home, and even if you just have a short time, as has been the case since we now have 2 young kids. Plus you can make it romantic, relaxing, whatever with music, candles, oils ... you can get into some fooling around or lull your SO into sleep ... I can't say enough about how great we have found that addition to our lives.
2. "Adventures" - we would pick one weekend a month, and take turns planning an "adventure" with a certain budget - something that you've always been curious about trying, etc. We didn't do anything too crazy - tried cross-country skiing, day trips, whatever - but it was fun either to be planning or to be wondering about where we were going and what we would be doing.
Some other things we've done in the course of our 12+ years together include ballroom dancing, learning to run, working out, as well as "dates" like going out to dinner, plays, movies, etc. It's not like we do this all at once, just taht for a phase of our lives we did some biking ... then we had the opportunity to do some travelling (and got hooked on that) ... then we both wanted to get in shape ... etc.
If you can find a good deal, travel can be a great way to re-connect and find new passions too. We've taken last-minute cruises and end-of-season prices for places like Portugal ... ah wonderful memories. I tend to drag DH to museums and creepy places (catacombs, etc) and he tends to drag me shopping and to cafes, to sit and watch the world go by.
I hope there's something int here to give you ideas about what would suit you & your DH best. It *is* possible to get through the kinda-bored stage - we hit it at about 5 years married - since then life has generally just gotten better

I look forward to seeing other responses to get some more ideas for us too!
All the best,
Andie