Console RPGs

It's not so much a matter of platform, it's a matter of style. The characteristics of console RPGs are about the following:

You control a party of three to five characters, four being typical. You will often start out with a single character and the others will join you later. In some games you can rearrange your party out of up to twenty members at will.
There is no character creation, each character is pre-made and has a distinct personality. Character development is pre-determined too. A notable exception to the first rule is the first Final Fantasy game, where you create a party of four from six D&D type character classes. You always get to name your party members.
Usually there is a distinct main character, though he is not always the first character you play. He is always male and nearly always a sword fighter.
Combat will be turn-based, though around the mid-90s games tended to pretend they are real-time. Colorful spell effects often make a good part of the fun of battle. The battle background will reflect the terrain you are currently on.
Enemies sometimes drop items, but always yield money along with experience points. This money and the equipment you can buy with it is as much part of character development as levels.
Gameplay is usually very linear, with new areas of the world map opened as you complete quests. Vehicles play a big part in this, since some areas will only be accessable with special vehicles. Later games often have pseudo-non-linearity in the second half, where you have opened up the whole map and have a couple of quests that can be finished in any order.

Action RPGs like Terranigma and the Zelda series form a subset with slightly different rules:

You control only one character. This is a natural consequence of the real-time, action combat.
This character will be a teenager living with his parents or single parent.
Instead of random encounters there are a few enemies placed on each map that respawn as soon as you leave and re-enter it.
You can buy, but never sell items, so be careful with your money!

Chronotrigger, while turn-based and party-based, follows action conventions for heroes and enemies, though enemies often are not visible when you enter the map.

Console-style RPGs for PC

Commercial

Commercial console-style RPGs are typically Japanese (sometimes Chinese) and ported from the PC-98.

Knights of Xentar: Actually Dragon Knight III, this is one of the best known and most popular console-style RPGs for the PC. Combat in this game is real-time and practically automatic, only casting spells and quaffing potions requires player action.
Cobra Mission: Though actually the better game, it is less popular than Knights of Xentar. Combat is real-time first person, the cursor changes to the equipped weapon, and the exact spot where you hit is significant. It is the only console-style RPG I know that has an ammo system.
Mad Paradox: This game suffers under a near-lack of randomization making battles all too predictable. Combat is turn-based in a sort of over-the-sholder 3rd person view.
Princess Maker 2: While this game is not an RPG, you can make a fighter out of your character and adventure in console RPG style.

Amateur

99% of all amateur RPGs fall into one of two categories: Console-style or imitating the Ultima series.

Aspetra: A strange and somewhat amateurish, yet amusing game. I played it right to the end, and wrote a full review.
Avalon: Not much to say about it. I played the first three chapters and took lots of screenshots, but lost interest.
Mysterious Song: When I tried to play it the first time, I found the initial battles far too hard to give a decent chance to survive. Later I tried again, and had no problems, but got bored after a while.
Slime Forest: This game is mainly intended to help you learn Japanese.