Jelly fungi represent some of the most primitive clades of Basidiomycota, two groups of them in classes by themselves far removed from the Agaricomycetes class where you find most fruiting bodies. Their simple gelatinous texture allowed them to survive periods of dry weather and then to reconstitute themselves during the next rain, before complicated structures like a cap and gills had evolved. They have unique microscopic features as well... the Tremellomycetes have basidia that are divided or "septate" longitudinally, and the Dacrymycetes have bifurcated basidia like a tuning fork as well as spores that are divided by septa into sections. These features are shared by some of the most primitive mushrooms of the Agaricomycetes as well, which also have a jelly-like consistency. You will find such primitive species in the orders Cantharellales, Sebacinales and Auriculariales as explained on my taxonomy page. As is common with the flasks, (among others) some of these jellies are capable of reproducing asexually as well as sexually.
The Ascomycota phylum has also evolved jelly-like mushrooms, similar-looking yet not at all related to the other mushrooms on this page. They are not "primitive" but represent an evolved state that has happened several times. They usually don't have the same completely jelly texture, but some of them could be confused with Basidiomycota.
Sometimes gelatinous fruiting bodies are only a two dimensional crust of soft material on wood and will be found on the crusts page. Species covered on this page are a little more three dimensional. I don't know of any poisonous jellies, but they have not been well studied. They are mostly tasteless but can add an interesting texture to trail mix. Any attempt to cook them will probably result in them vanishing into nothing in the frying pan.
Unfortunately there are many similar looking jellies, hard to tell apart, so I recommend browsing the whole page before making a determination.
Tremellomycetes - Literally in a class by themselves. The yellowish folded species are commonly known as "Witch's butter". They are parasitic on different crusts found on wood, most commonly Stereum, Aleurodiscus and Peniophora (all in the Russulales order) or even on some Ascomycota pimpled "flasks" in the Sordariomycetes class. You may or may not be able to see the host crust fruiting on the same log. Believe it or not, the meningitis and pneumonia causing Cryptococcus fungus is somewhat related to Tremella.
T. mesenterica (lutescens) - fewer folds, and more pale-translucent, on Peniophora on hardwoods.
T. mesenterella - as T. mesenterica, yellow-brown, usually on willow or dogwood on Peniophora.
Syzygospora effibulata - related, but not looking similar, is a waxy film that coats galls that can form on Gymnopus dryophilus.
Dacrymycetes - also in a class by themselves. Saprophytic on wood, unlike the parastic Tremella. The large folded species are several cm or more in extent. The smaller blobs only several mm. Most of the rest of the yellow-orange jellies are found in this class but most other colours will be found further down. Dacrymyces species themselves do not usually have a stem, but some related species do.
D. chrysospermus (palmatus) - conifers, folded, often more orange than Tremella aurantia, with a white point of attachment.
D. stillatus (deliquescens) - the species most likely to look like tiny cushions (like dots) on conifers.
D. ovisporus - the species most likely to look like little orange brains on conifer wood. Also see Craterocolla.
Other relatives of Dacrymyces, all on wood, somewhat more stemmed:
Heterotextus (Guepiniopsis) alpinus - our largest top-shape, <1cm, on conifers near snow melt.
Heterotextus luteus - smaller on conifers, (<8mm), elsewhere, both larger than the Dacrymyces chrysocomus grp.
Ditiola (Femsjonia) peziziformis - top/
Calocera viscosa - coral like Clavulinopsis corniculata but pointier, on conifers, less brittle. <10cm high, <2.5cm across.
Agaricomycetes - these jellies are not in a class by themselves, but in the class with most other Basidiomycota. They share some unique microscopic details with the other jellies, meaning they have not evolved far from them. The Auriculariales order contains most of them. Saprophytic.
Exidia candida - translucent whitish blobs discolouring orange-brown, larger than Tremella globispora, etc., sometimes in expanded masses.
Myxarium atratum (nucleatum) - translucent mass of pustules covering <10cm, "seeds" embedded in jelly. See Efibulobasidium.
Craterocolla cerasi - pinkish orange discs that become brain-like jelly and up to 5cm across, larger and more convoluted than Dacrymyces ovisporus. On shredded inner Populus bark.
Efibulobasidium albescens - white translucent pustules <3mm across on herbaceous stems, similar to Myxarium.
These are Sebacinales.
Sebacina epigaea - white pustules converging to become a flat waxy, jelly crust. In the Sebacinales order. See also Tremella globispora.
Ascomycota - the following jellies are completely unrelated and belong to the Ascomycota, the first two in the Pezizomycetes where you find the large cups and the others in the Leotiomycetes class, where you find some small cups and earth tongues (just as you might guess from the general habit of the Pezizomycetes growing on the ground and the Leotiomycetes growing on wood and being more frequently small).
Pseudosarcosoma (Sarcosoma) latahense - smaller, <5cm, young top surface somewhat purplish-black, thickened base somewhat gelatinous
Bulgaria inquinans - black jelly cushions on hardwood, not convoluted like Exidia glandulosa and with a brown scurfy exterior when young and black spores that stain your hands. Related to some earth tongues. (Leotiales). Plectania melastoma is similar but not gelatinous.
Ascotremella faginea - big
brown brain on hardwood. Related to some