While playing various RPGs I've come across die rolls that aren't covered by #d# + #.
Other forms of d notation
Can subtract from a roll result e.g. 1d6-2. What happens if result is zero or negative depends on rules system. GURPS 4th Ed may have zero or one as the result depending on circumstance (page 378).
Can multiply the roll by a number E.g. 1d10 * 10. These tend to be in specialised circumstances like treasure and massive damage.
May add together different die types Earthdawn step 9 is d8 + d6. Step 40 is 2d20+d10+d8+2d6 (page 36)!
I have played several non-d20 games. Here are some of the ways of dice rolling I've encountered.
Rolling against a target to determine succeses. Each die is individually compared against a target; those that reach it are deemed a success. E.g. d10 against target 7 in Adventure! (pages 111 - 112). (I recall something similar in world of darkness) d6 against target of 4 in Albion and Legends Walk!. The dice may also explode (see below) granting extra dice to test against the target.
If the highest result on the die is obtained, then another die is rolled. If summing dice then it is added on to the original result and counts as a single roll. If the highest result is obtained on the extra die then another extra die is rolled etc.
If counting successes against a target then extra dice are individually compared against the target and may give extra successes.
Spycraft 2.0 (d20 based) - in a dramatic scene the GM's action dice also explode if a 1 is rolled (page 424).
A particular number are thrown , but the player can only keep a certain number; the rolls of the chosen dice (almost always the best ones unless the player is trying to pull a blow) are added together for the final result . 7th Sea only uses d10s so it has a notation of 5k2 roll five keep two. The dice can explode as well in this system. The explosions are done individually and are treated as a single roll before selecting which ones to keep (pages 17-18 ).
d% is a common alternative notation to d100.
Systems that only have one type of dice often omit the number of sides and just use d, e.g. 6 sided in Gurps.
d is used in English because it is the fisrt letter of die/dice. In Germany w is used for the same reason, so 1d6 is written 1w6.
Amber avoids all these problems of notation
Some systems use playing cards froma standard deck with jokers. E.g. Deadlands and 50 Fathoms. (The former uses them to form poker hands to see who wins!)
What others are there out there?