I'm using Ubuntu Linux with an unmodified Swedish layout. It came with lots of symbols on the RAlt (Alt Gr) layers, plus I also have the Compose key enabled to get even more. Often, the Compose combos are more intuitive.
These below are all actual mappings that I have found and use:
RAlt + Shift + 0 ⇒ °
RAlt + Shift + 1 ⇒ ¹
RAlt + Shift + 2 ⇒ ²
RAlt + Shift + 3 ⇒ ³
RAlt + A ⇒ ª
Compose 1 2 ⇒ ½
Compose 1 3 ⇒ ⅓
... and so on
RAlt + C, or Compose O C ⇒ ©
RAlt + R, or Compose O R ⇒ ®
Compose T M ⇒ ™
RAlt + 3/4/5/6 ⇒ £ / $ / € / ¥
RAlt + E ⇒ €
RAlt + Shift + E ⇒ ¢ (Euro-Cent)
RAlt + Shift + Y ⇒ ¥
RAlt + M ⇒ µ
Compose , C ⇒ ç
Compose A E ⇒ æ
Compose O E ⇒ œ
RAlt + Y/U/I ⇒ ←/ ↓ / →
Ralt + Shift + U ⇒ ↑
Compose - > ⇒ →
Compose < - ⇒ ←
Compose = > ⇒ ⇒
... but ...
Compose < = ⇒ ≤
Compose + - ⇒ ±
RAlt + * ⇒ × (actually, RAlt + Shift + ')
Ralt + / ⇒ ÷ (actually RAlt + Shift + 7)
Compose . - ⇒ ·
Compose . = ⇒ •
Compose - - - ⇒ —
Compose < > ⇒ ⋄
Compose : ) ⇒ ☺
Compose : ( ⇒ ☹
Compose < 3 ⇒ ♥
I am missing ▲ ♫ ★ ✓ though. Maybe I just haven't found them yet.
In Swedish layout, diacritic marks " ^ ~ ˇ ' ` are available on two dead-keys.
Some characters above created with Compose are also available on a RAlt layer but the locations are not as intuitive.