Dun1 Loc: Atlanta, GA

The first rule is do not leave any batteries in your flash, especially if it's not being used.
I have use a Canon Compact Battery Pack CP-E4N to power my flashes, it saves on recycle times. I have used Sanyo Eneloop, and Power X NIMH batteries.
For many years I preferred Duracell Alkaline batteries, I have found that they seemed to be prone to leakage versus other Alkaline battery brands. I use Alkaline batteries as back up batteries.
If you follow his advice of Gary Fong, he says using an ISO setting of at least 800 will reduce flash recycle time and prevent overheating

bkyser Loc: Fly over country in Indiana

Lee, I see some answers from some of the regulars from the wedding section, but you may want to post there to see if any more people from "the peanut gallery" want to chime in.

Here's my take. First, If you up your ISO, and open your Aperture, you shouldn't be anywhere near full power flashes, which will speed up your recycle time. My flashes recycle almost immediately, because they are only shooting at about 1/8 to 1/4 power.

Next as far as battery choices. I use only eneloop pros in my flashes. I put in a fresh pack between the getting ready shots, and the ceremony shots, then again between the formals and the reception. I keep them in individual baggies, so I don't break up sets. That way, IF I happen to run a flash down, I can keep the sets that are evenly drained to put back in. The sets are usually still close to full, but during a wedding, I don't take any chances. I also have second shooters, and bring a total of 6 flashes, 3 bodies, etc...
It may seem like overkill, but again, you can't say "hold it, I need to change my batteries" during a wedding, and you certainly can't risk missing important shots of a hopefully one time event.

I did try to save a few bucks and got some Amazon Basics batteries that were rated the same as Eneloops. I used them one time, and although I charge them, they are kept in my bag as back up as a last resort. They drain quickly, at least mine did. I'm not "technical" but I believe it's not a capacity issue, but it isn't able to hold up to the fast drain that a flash can put on them. Just my 2 cents.

Spirit Vision Photography Loc: Behind a Camera.

While shooting weddings every weekend, sometimes two or three per weekend, I found the alkaline not up to the task. As you use them, the recycle time of your flash quickly declines, meaning missed shots waiting for your flash to recharge. It would sometimes require two or three sets of almalines to complete a wedding and reception. However, once I switched over to the rechargeable Eneloops, thing became MUCH better. Much quicker recycling time for my flash units, and one set of Eneloops will get me through an entire wedding and reception. Used with a quality battery charger, the Eneloops have lasted for years. I also discovered that Duracell Coppertop batteries are much more prone to leaking than other brands of alkalines.

KK

jimvanells Loc: Augusta, GA

You might want to try the lithium batteries. They do not slow down anywhere as much as the alkaline batteries. They pretty much run full out until they die. The best option is to buy a belt battery pack for the flash, every wedding photog has one or two.