In addition to the fortified (resembling the plan of a 17th or 18th century fort) and non-fortified (wavy type banding), I've incorporated those mentioned with some other types that come to mind:
BANDED
· fortified (bands enclose a large area, resembling the floor plan of a 17th or 18th century fort);
· plain banded (a pattern of wavy lines);
· lace (lots of enclosed bands);
PATTERN
· dendritic (tree or shrub-like branching formations);
· plume (ostrich feather-like formations);
· moss (thread-like formations);
· picture, landscape or scenic (combination of patterns that resemble landscape paintings);
· orbicular or eye (contain ball-like inclusions);
· poppy agates (I'd include the so-called "Ocean Jasper" and some translucent poppy-type jaspers as agates);
· cloud (very soft, fuzzy bands and swirls);
· flame (fire-like plumes);
· waterline or onyx (parallel horizontal banding);
· Fischer (an artificially induced dendrite-type formation);
OPTICAL PHENOMENA
· iris (very, very tight banding that breaks light into a rainbow spectrum when backlit)
· fire (botryoidal formations containing thin layers of iridescent goethite and/or limonite);
· parallax or "shadow" (banding in transparent agate that gives a 3D effect);
· turtleback (botryoidal formation with very fine/invisible banding that forms a turtleshell type pattern when backlit);
FORMATION
· geode (a roundish thunderegg, vesicular agate or similar with a hollow center);
· thunderegg (a rhyolite nodule in a volcanic flow in which a gas chamber later filled with agate, often under great pressure);
· botryoidal or grape (resembles a grape-like cluster of orbs);
· mammillary (resembles udders);
· enhydro (contains bubbles of ancient water);
· vein or seam banded (pattern follows the outline of the crack which held it);
· amygdular (roughly round agate or geode formed in gas bubbles within volcanic host rock);
· membrane (filled with broken bits of the initial banded layers);
· polyhedral (a type of agate replacement where the agate follows the form of a previously dissolved polygonal mineral crystal);
· polymorph (agate that has replaced another mineral);
· sagenic (agate containing sagenite-type needles);
· agate casts (limb, bone and similar casts of once-living organisms);
· oolitic (contains small orbs; orbs larger than 5mm are pisolites, rather than oolites);
· brecciated or shatter (fully formed agate that has shattered and then re-healed);
...probably more. And it probably should be mentioned that some agates are combinations of two or more of these features.