I haven't found a lot written about how other sports affect one's tennis, so most of what I write here is based upon personal observation of my tennis students and experiments with my own game. One point on which a well-published consensus does exist is the general benefit of participating in a variety of sports. No one sport can produce every benefit that sports can offer, and tennis ranks well below many other sports in some key areas.
In terms of total body conditioning, for example, tennis is easily surpassed by cross-country skiing, the best sport on this criterion, and swimming, a more popular contender. Each sport makes different demands in terms of the muscle groups, types of energy metabolism, coordination skills, and mental focus it employs. One could justifiably rank tennis near the top for developing coordination and concentration skills, but underneath an overall ranking lie important differences in the kinds of coordination or concentration involved. Gymnastics, for example, requires very high levels of coordination and concentration, but these attributes when used to execute a difficult vault or tumbling sequence are significantly different from those needed to react to a 100 m.p.h. serve.
Reacting to a hockey puck though, is very similar to reacting to a tennis ball. In both games, you use precise footwork to gain good position and your arms to execute contact with a small, fast-moving object. Unless you're the goalie, hockey also provides a vigorous workout with intense bursts of energy expenditure like those used in tennis, but at a greater frequency and with more activity between bursts. The dry-land forms of hockey, such as floor hockey, field hockey, and roller hockey, are as beneficial as the ice game. When I do see other sports recommended for tennis players, hockey is always rated highly, and I would concur by rating it as the best complement to tennis. I base this both on theory and the real-world observation that my hockey player students tend to learn tennis faster than athletes coming from any other sport.
Interestingly, soccer also ranks well as a tennis complement, despite barely using the arms. Tennis strokes are built upon good footwork, and soccer is unequaled in developing coordination of your feet. It's also, especially for midfielders, superb exercise, combining both aerobic and anaerobic energy expenditures.