Plus running mono you can gain the added benefit (if your amp & speakers are able to handle it) of more power by bridging the amp.

My amp is spec'ed at 800W into 4 ohms in bridged mode (Behringer PMH3000). I have two speakers with Speakon connectors (Behringer B1520), and I see diagrams where they are chained together for mono operation.  Is this a normal capability, and is it possible to connect them in parallel to lower the impedance of my two 8 ohm speakers to 4 ohms?

I wish there were a "Live Sound for Dummies" book to get me started. Not that I am a complete dummy, but I find a great lack of explicit information available about speaker hookups.

I also wonder about the connection of the Speakon connectors, since their pinouts are quite different. With my Samson power amp used for a floor monitor, I can use a banana plug that is connecting one pin from one channel and one from the other to change the pinout for bridged mode. But I don't know what the equivalent thing is for Speakon; is there an adapter jumper or something?

You have to make sure your amp can handle a 4 ohm load in bridge mode.  Some amps can only go as low as 8 ohms - and I just looked at your amps spec sheet & it can't go lower than 8 ohms so connecting both speakers in bridge mode isn't an option for you (unless you really want to get into different wiring like series and raise the load to 16 ohms, but then you are defeating the purpose of bridging for power).  If your amp has banana plugs (most amps do & use both positive terminals for the actual bridge connection), i'd just get a couple banana to speakon adapters & use that instead of trying to rewire your speakon ends to work in bridge mode.

Both ends are speakon, so I think I would have to rewire anyway. It seems there might be an easy way to make an inline adapter to hook in parallel, but I don't see parallel wiring mentioned anywhere out there on the net in regard to live sound. It seems it would make sense to do it sometimes, but it doesn't seem to be done. Strange.