Unless you are quite good at a particular sport, the best way to improve your conditioning for that sport is to practice that sport at high intensity. If you flag during judo randori, do more randori; if you get winded while boxing, then hit the bag more; if your aikido conditioning is poor, then go to aikido class more often, and make sure those classes are intense enough to be challenging.
In some sports, people can get so efficient at the skills involved that practice doesn't improve their cardio much. This is particularly true in sports like Brazilian jiu-jitsu, where a black belt often doesn't have to expend much energy to fend off or tap a white or blue belt. In these cases, using other forms of cardio to improve your conditioning can be productive.
I found it helpful to understand the three metabolic pathways. Humans burn energy differently in (and recover differently from) different lengths of exertion:
See this question on Fitness.SE for a more detailed explanation.
Intervals in any form are very productive for increasing your "wind" for multiple bouts of randori. This includes sprints, Prowler pushes (PDF), kettlebell work (swings, clean-and-jerks, or snatches) and a variety of other work. The key is that allowing yourself to recover partially or totally between exertions allows you to train the explosive phosphagenic and hard-but-brief glycolytic pathways in addition to the steady-state, slow-and-plodding oxidative pathway.
You can also just do a single brief-and-hard workout on the order of 5 to ten minutes of all-out effort. Glenn Pendlay has weighed in on the most effective conditioning for combat sport (which is tangentially related to aikido):
Remember, the goal is overall strength and condition, not to get good at any one particular thing. Find 5 or 6 exercises that work for you and rotate through them, using one per workout. Keep track of the reps you get in 10 minutes on each exercise, and try to improve. Here are some good ones…
Push a prowler.... Kettlebell clean and jerks.... Farmers walk.... Take a barbell, a light one, and keep it moving without setting it down for 10 minutes....