Here's a biggie: A CRPG is what you make it.
Every time you are given a choice within a game, you are given another choice alongside it. You are not just given the choice to go to location A first, or location B, to blag your way out of a fight or get stuck in, to behead the traitor or forgive him. You are also given the choice of whether or not it is a roleplaying game.
That is to say: you are given the choice to do what will get you the most in-game benefit, or do what the character you are playing would do. The two are not always mutually exclusive, but there will often be times when they don't match up.
Here's a fairly hefty and generalisation filled chunk of example.
Most games presented as CRPGs (certainly in the non JRPG mold) have a slew of exciting things you can do away from the major storyline; running errands for lazy townsfolk, hunting, working for law enforcement or other organisations, etc. These will net rewards, in the shape of cash and kit, they may affect the way various factions in the game percieve your character, and in most cases they will also provide either XP in themselves, or extra opportunities to earn XP to advance your character's stats.
They are also, it should be remembered, a fair chunk of the content you paid for when you bought the game.
But are they what your character would do?
There are some games where there is genuine in character encouragement to get out and bimble about doing stuff. Morrowind, for example, opens with the PC being sent to meet a contact/handler in a foreign town, who informs you that he wants you to get out there, blend in with the locals, make a bit of a name for yourself and get trained up and kitted out before he'll set you on the mission the powers that be have in mind for you. The main plot situation is simmering, but has been for years and there's no great rush to fix it, just a sense that it needs fixing at some point in the not too distant future. Obviously there are still IC decisions to be made about what quests to take, who to side with in certain situations, etc, but the decision to do sidequests and level up seems natural because you've been told, in character to do so.
One of the biggest problems I had with it's sequel, Oblivion (a game which I should point out that I adore none the less, more on why in another post...) is that the opposite is true. There's a crisis happening right now, lives are being lost, you have a job to do saving the world, so why would you involve yourself in tales of adultry, petty theft, and sexual harrassment in the mages guild?
Then, of course, there's Mass Effect 2. Oh what a beauty. There are plenty of sidequests that pop up in the game -many of them designed to have an emotional connection for the PC- in between the main missions to assemble and ensure the loyalty of a team of high-end misfits. You'd better prioritise them carefully though, too much faffing about at the wrong times can lead to pretty serious punishment, although that punishment only carries any weight if you're emotionally invested in the story and the characters.
So you only have to think like a roleplayer if you're roleplaying.