I usually let a first time player choose their race and class. I let them roll an extra d6 on the important stats. so, for a thief on DEX, roll 5d6 choose the best three.
experienced players I make roll 4d6 for each stat in order. then form a character by the numbers.
I also make sure that 1 and 20 rolls never get ignored. A natural 20 will always lead to something great happening, even if its rolled on a perception check, or saving throw. A natural 1 will always have consequences.
My favourite trick, is when a halfling rolls a 1, halfling luck kicks in, I make something bad happen to whom or whatever is standing closest. Maybe an enemy, maybe a friend.
Good thing to know. I will stay away from Halflings.
yeah!
I like those biases and superstitions working their way into role playing.
when they brought out dragon born as a playable race, I made a ranger who's "prefered enemy" was dragon born. He was like Archie Bunker in the woods.
Interestingly, in 5th-edition, full hit points for 1st-level characters is the RULE-rule. 
On that note, I'm happy to say that the newest edition of D&D allows me to play closer to the book than ever before. In fact, I'm hard-pressed to think of a place where my groups deviate...
One rule we often "bend": If you have Inspiration, you're technically supposed to decide whether or not your going to spend it (i.e. to roll a 2nd d20 and take the better of the two results on your attack or skill check) BEFORE you roll. In our group, we'll sometimes let a player burn their Inspiration and roll the 2nd die after seeing the crappy result of their first roll. That's about it though! Not like in the old days...
I can't even begin to remember/list all the ways we bent AD&D. House rules were the only thing holding that hot mess together. Gygax was a vocal hater of critical hits, so that was always a house rule... And if anyone at MY table even brought up the topic of "alignment languages" they were banished from the group. 
We use critical hits and fumbles in our AD&D games, it adds an extra bit of fun(?).
Good to hear from you Mike, sounds like you are getting regular doses of 5e D&D.
And don't get me started on alignment languages, we scrapped them really early on.
I am thinking of running my next ad&d campaign btb just to see how it pans out.
For inspiration, I have two gold metal d20's. I give one to a player when they earn inspiration, and they "spend" it, by rolling it. anytime they want. or they can give it to another player (or even an NPC) in time of need.
Do you play BTB (by the book) or do you use your own house rules when playing D&D? I know in the nearly 40 years I've been playing we've had numerous house rules, some of which have fallen by the wayside. I thought this would be a good place to post and discuss your house rules. I guess the most obvious one is full hit points for first level characters.
Another we've adopted is when rolling a new character we don't start recording the stats until the player rolls a 16 or more.
Changed the title to include all weird things us DMs do