Here are a few that I've found that seem to work nicely on the complex sounds of a 12-string guitar:
Note that all the software here is running on Linux (an Ubuntu distro) and I don't know how much is applicable to other operating systems. Jack is a low latency audio server that runs on Linux.
The information here about convolution is applicable to most audio systems, and the Freeverb plugin is available on most platforms.
Calf Reverb Plugin
I've read good things about the Calf plugin but I usually use Audacity, and the calf plugin doesn't seem to communicate well with that sound editor. But because of one thing and another, I started using Ardour (ardour.org) and the Calf audio plugins, which seem to prefer jack connection applications over LADSPA, work great in Ardour.
The default reverb settings for the calf plugin use zero pre-delay. The buzz saw sound that takes over my guitar from software reverb seems to come from "pre-delay" (some reverbs call it "early reflection").
When I went back to try some other LADSPA plugins like Gverb and FreeVerb without pre-delay, they sounded better. But I think the calf plugin is better sounding - very smooth and natural.
So point one when adding some 'verb to the 12-string is to "can the pre-delay".
Convolution uses the actual sound of a place like a church or concert hall to modify the audio file that you record. So for the home recording guitarist who mic's the guitar real close and finds the resulting recording sounds too "in your face", this adds a nice bit of roominess around the guitar. There aren't many settings you need to change for convolver reverberation...I guess you can delay it; you can scale how much you include in the mix.
There are gigs of Impulse Files free on the 'Net. Here at SpaceNet.org.uk, for example, are some that were generated in rooms with very long reverberations. The Hamilton Mausoleum is the longest. And it is very smooth.
To run this on Linux, I'm using Jconvolver software created by Fons Adriaensen, an acoustic engineer who has done a lot of interesting acoustic research and written some very nice music software open source.
You can see (and hear) a short video I made of a desktop session where different kinds of reverb are applied via Ardour to a 12-string guitar practice session here.