I would have to say that Baboquivari Peak is the most desirable summit in Southern Arizona. The approach is arduous, there is no non-technical route to the top, the view and surroundings are very special.
The first trick is to get there. Drive to 3 points and head south towards Sasabe. Take the first right after milepost 16 and drive to where a gate blocks the road and a ranch house ahead is visible. The road may now be gated further from the ranch-house. The last time I was here, the Nature Conservancy seemed to be in possession of the premises. From here you hike up Thomas Canyon to the big saddle to the right of the peak. Plenty of opportunity to get off the trail and bushwack through miles of catclaw on the way. Water can be hard to come by - this is not optimal for a summer visit.
Many parties camp in the saddle, and if so, what I have always done is to head back down the trail to where the path over to the north end of lions ledge takes off. This leads you left up a rocky gully and across rock slabs to the ledge. Lions ledge itself is worth a visit, it is an amazing spot with cliffs above and below.
As for routes, I have been up the Forbes route, Don's crack, and the Southeast Arete. The later is the classic, and there are 3 reasons: location, location, and location. The SE arete is 7 pitches or so of 5.6, and is a climb that you should do early in your climbing career when it can be a real mountaineering adventure. It is a route I have done many times, and will probably do again, at least once I am in the mood to haul a heavy pack up that trail again.
If you are out to climb the southeast arete, get up onto the north end of Lions Ledge, and cross the ledge to the south, passing the spring and cave. Admire the giant dihedral and crack system which is Don's crack, and then continue just past the arete itself so you are on Lions ledge on the South side of the peak. as soon as you do this, be on the lookout for a chute in the midst of trees that you 3rd class up (some might want a rope here) to where you belay for the first pitch. At this point you are on a sort of saddle with views both south and north.
Now you have the option of descending the Forbes route on the west side of the peak (which could present some routefinding challenges if you have never ascended the Forbes route), or rappelling the SE arete, which I have done on a number of occasions. Rapping the route has always been a sensible option to me, but I am positively sure you could get into big trouble doing this, so if you have any doubts, don't. You would need to have two ropes. I never had to worry about other parties below me, but your circumstances could be different. If you have gear down on Lions ledge, descending the SE arete would make even more sense.
Tom's Rock Climbing Info / ttrebisky@as.arizona.edu