Most of the time, the only question that matters is "Did character X accomplish task Y without screwing it up?" and anything beyond that is gratuitous detail. I don't need "degrees of success" beyond YES or NO for situations like that.

However, if it matters, then I'll use some form of "degree of success" system when it's called for. I've been running Savage Worlds lately, and the "Success and Raise" mechanic handles this quite well. If the PC's are in a hurry, a raise means they're done in half the time. On attack rolls, a raise means extra damage. (The equivalent of a critical hit.) Extra raises are just gravy; the players get to brag about how awesome their roll was and high-five each other.

This is something I've been working around with a current project. Flyingmice has an excellent point about damage being a measure of success. Some systems do a better job of integrating this into the rules than others. D&D for example has a, mostly, binary attack roll with damage being independent. The exception to this is of course critical hits. Alternatively, Eclipse Phase has some unique mechanics for boosting damage based on the roll and on the actual margin of success compared to character skill.  

That said I think the core of this thread falls more towards non-combat rolls. How do you create logical tiers without bogging down play. Games PbtA are explicit on the character sheet on how to manage partial success keeping game play fast. As mentioned the X over target  some games use also make for a quick reference as long as you have a solid grasp of what each degree means.

Quote from: Baron Opal;815684...
The closest I've come would be combat rolls in Rune Quest. Since you have your critical numbers set before the session, and they won't change, it was pretty easy to use.

IIRC your critical ranges are based off of modified or actual % chance not your base. IIRC this is also how BRP uses specials and criticals.

Quote from: trechriron;818189IIRC your critical ranges are based off of modified or actual % chance not your base. IIRC this is also how BRP uses specials and criticals.

That's right for RQ2 and 3. Typically the critical range doesn't change unless you are close to edge of a step, but the range for a special probably will change a bit. A simple lookup table can be consulted if you happen to roll low which makes it easy or for the arithmetically inclined one can just calculate the resulting 5% and 20% chances in one's head. Most of the time the roll will clearly be a simple success or a simple failure so you only really need to know the chance for a critical, special, or fumble if the roll is on the low side or the very high side.