What status of oven do Crockpots, electric plates, and water boilers have today?[1]

Adjustable temperatures: If they have adjustable temperatures, they have the same status as stoves and ovens, and must be covered in order to leave less than half cooked foods on them before Shabbos.[2]

One setting: If they have only one setting, either on or off and it is thus impossible to higher or lower the temperature, they never need to be covered.[3] This applies likewise to an electric water boiler that only has one setting.[4] However there are Poskim[5] which are stringent in this matter regarding water boilers.[6] [To note that boilers with Shabbos setting are considered to have adjustable temperatures and hence the water must be cooked to the point of Ben Drusaiy before Shabbos begins.]

Attached to a timer:[7] If the electric plate, crock pot etc. is attached to a timer which turns on and off constantly on Shabbos[8], then even if the electrical device itself contains no adjustable temperatures seemingly it has the same status as an electric device that does contain adjustable temperatures, and hence must be covered in those cases where Ketumah is required.[9]

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^[1]  Shabbos Kehalacha Vol. 1 pages 298-300; Piskeiy Teshuvos 253:7; SSH”K 1:25

[2] Although electric plates, boilers and crock pots are covered by metal, and hence are physically similar to a gas stove with a blech, nevertheless since the metal is constantly there, without one doing any action, it does not serve as a reminder against raising the flame. In a similar case of doing Chazara to a heater in 253:26 Admur brings a dispute regarding if we consider the constant metal covering deemed as Ketumah, and he rules to be like the stringent opinion. [See Piskeiy Teshuvos 253:5]

[3] Shabbos Kehalacha Vol. 1 pages 298-300 permits in all cases; Minchas Yitzchak 5:91 and Shevet Halevi 5:30 permit regarding a water boiler; Piskeiy Teshuvos 253:7 and SSH”K 1:25 only permit in a case of that the electric plate is meant for warming and not cooking. Vetzaruch Iyun as to the reason behind this differentiation.

The reason: Now although it is possible for one to remove the plug from the socket, nevertheless we do not suspect one may come to lower the flame, but rather only to raise it. [See Igros Moshe 4:74-25]

Other opinions: Some Poskim are stringent to require a cover by all electric plates even if one cannot change the heat setting. [Shvus Yitzchak 8 in name of Rav Elyashiv] 

[4] Minchas Yitzchak 5:91 and Shevet Halevi 5:30; Shabbos Kehalacha ibid

[5] Igros Moshe 4:74-23

[6] Perhaps this is for the reason mentioned by the questioner there, that one may come to remove water from the boiler on Shabbos prior to it being fully cooked, and doing so is forbidden due to hastening the cooking. However such a logic seems puzzling as we have no precedent that the Sages ever suspected of such a matter, and from the clear rulings it is implied that the opposite is the case.

[7] Authors note

[8] Such as one set up his electric plate to turn on for half hour intervals in order to keep his food warm, and not burn the food.

[9] As we suspect one may come to adjust the time in a forbidden way in order so the food be ready on time.