Do you play it RAW?

TLDR: rules-as-written (RAW) means different things to different people. Here are some distinctions that I think make sense.

Rules-as-written, or RAW, as most people like to write it. What does it mean?

RAW
Rules as Written. Used literally, it means whenever you have a question about how to play you follow what the rulebook says to the best of your ability. If you make a ruling at the table and a player looks it up (either right then or after the game) and finds a contradiction between your ruling and the text, you go with the text. It also means, in a literal sense, that you aren't subtracting, adding, or modifying the rules in any way.

RAI
Rules as Intended. It's pretty hard to play any game like that. There are bound to be some awkward and unclear phrasings, typos, or missing rules that make playing RAW difficult. RAI means that you stick close to the rules and play them as you believe they are supposed to be played. You are not adding, subtracting, or changing the rules unless there's clearly an error in the text, a rule is unplayable (wasn't play-tested), or you have to fill in a gap where the rules are silent. When you do fill in a gap, you do it by following the logic and spirit of the rules. You aren't inventing so much as extrapolating. Personally, I still consider this RAW, especially if the rules encourage you to invent/fill in the gaps.

Rules+
Taking another step away from RAW is adding things that don't obviously change or interfere with existing rules, but clearly weren't intended by the original rules either. Let's call this Rules+. For instance, you bolt some kind of sanity mechanic onto Oe D&D or a house rule like "shields shall be splintered!" The thing about adding rules is that no matter how careful you are, you are affecting existing mechanisms and play style. Perhaps adding a Sanity mechanic makes the Intelligence ability score in D&D less important. Or shields shall be splintered means that every character now carries a shield and leads a donkey with half a dozen extras. Adding rules is a slippery slope, especially if what you liked about the original rules set was their "simplicity." 

Rules –
Clearly, if there is a Rules+ there is a Rules–, meaning you drop some rules because they feel clunky, slow down play, aren't meaningful, etc. Subtracting may reduce complexity, but you may also be throwing out the baby with the bathwater. As with adding rules, you can quickly find yourself playing a different game. For example, the Save progressions are part of class strength and weaknesses in old school D&D, as well as a way to differentiate between the peril of various threat types. If you dump those in favor of straight roll-under ability tests or a single save, you may be losing one of the classes' primary advantages (good Saves) or negating one of its drawbacks (bad Saves). Further, streamlining Saves means dragon breath, poison, and rays are all roughly the same type of threat and equally easy/hard to avoid/resist.

Breaking RAW

When you get to the point of doing lots of Rules+/- and even rewriting rules to work differently, especially if they are core rules like how spells are cast, you have left the path of RAW. For instance, changing the spell casting in D&D to work off of "mana points" is not playing RAW. There's nothing wrong with it, and you are still basically playing D&D, but you almost need to put quotes around it. It's the kind of change(s) you have to let players at your table know about right from the outset.

So, Are You Playing RAW?
It's my opinion that if you are doing literal RAW, RUI, or perhaps even a small amount of Rules+/-, you are still playing RAW. It's a matter of not believing you know more than the designer of the game and taking care to try the rules as written first, before you make any adjustments or outright changes. Any such adjustments or changes should be governed by making the game play to its strengths, rather than making it feel different or fit a different style/genre of play. If that isn't your mindset, then you probably aren't playing RAW. Not that there's anything wrong with that.