"A Computer RPG is a game where you control a character or characters, that have values defining their in-game abilities (both innate and learned, usually called attributes and skills, respectively), which can be improved in the course of the game (by experience and/or training). Also, a CRPG has multiple different quests/missions for your character(s) to accomplish, that take place in a persistent game world, which you are (more or less) free to explore."
Now, I'm not overly satisifed with that definition, but it was the best one I could come up with, while still keeping it to two sentences only. Note that I do not mention character creation there. IMO, it is not absolutely required to have character creation in order for a game to be a CRPG. However, it must have defined values for your character(s) and have character improvement to be a CRPG. In other words, you may have a character and his/her starting abilities "imposed" upon you, but you must be free to advance him/her how ever you like (within reason) once the game starts.
I juggled for awhile with an idea of adding a sentence about the role of player vs character abilities, but decided against it. Instead, that became the major deciding factor in the subdivision of the CRPG genre. That being the division between "True" RPGs and "Action" RPGs. IMO, an Action RPG is any CRPG that places emphasis on the player's skills with the mouse (or whatnot) over the skills of the in-game character. In a True RPG, it should not matter one hoot how good my mouse arm or mouse-click timing is, when determining e.g. the results of a battle. Instead, the results should be determined by a ruleset, the character's abilities and (virtual) dice rolling - plus of course how well I lead and command the character(s) in battle. As an example, using these definitions, Oblivion is an Action RPG and NWN2 is a True RPG. (I know that the term "Action RPG" is applied a bit differently in the game media, but it was the best term I could come up with. I could have used "Action-Oriented" RPG, but that seemed too cumbersome. IMO, Diablo and its clones, what the game media calls Action RPGs, should be called something else altogether. Run and Kill RPGs, maybe?

Heh, all this text and I still haven't even gotten to my topic. What makes a CRPG good? To be honest, I do like both subgenres, True RPGs and Action RPGs, so it's not the control-scheme that matters to me. Hmm, I guess two things that I really like in a CRPG are 1) non-linear gameplay that is open for exploration and 2) emphasis on the game's story and lore (i.e. the story of the game world itself). If the game succeeds in these, it usually is good in my book. Of course there are other things, like how easy the interface is (I hate clumsy UIs), how the game is balanced/designed and how well the game's story is actually told, but still if the game gives you freedom of exploration and a good story, I'm hooked. Naturally it also needs to have the qualifications that I gave for CRPGs above (and have them sensibly implemented). Note: Freedom of exploration doesn't mean a thing if there is nothing out there. Giving me miles of empty prairie isn't what I mean here. Exploration without content is wasted time.