If I don't have to go out of way to do it, I will. When I played WoW, I would gather ore, herbs, or leather as I leveled. And when I got the mats needed for my crafting professions, I would use/trade them and sell the leftovers. Made quite a bit of money leveling alts once I had my mains maxed (I had JC/BS, Alc/Enchant, and a Mining/Herb as mains), I would pick up a gathering profession and just sell ores I got while leveling. Made a nice chuck of coin. Got a Mechgineer's Chopper out of it. I also sold my extra elixirs. When I raided I would make enough for my 10 man group, and sell off the procs. I also ripped off randoms, I would give them what they gave me items for, and wouldn't give them the procs, unless they asked about them, or if they were friends to the guild.
In Skyrim I would gather anything I ran past between objectives. Can't say I ever USED any of them, but I remembered in Oblivion I chose Alchemy as one of my Primary Skills so I could control my leveling (I chose skills I could control or ones I never planned on using). Though, I never needed money in either game.
I can't say I really like it as a main focus for gameplay, but as a side thing it's not bad. Especially in an MMO where it can make you quite a bit of money.