Bubble Bobble

Amiga mainscreen

Bubble Bobble is a true Taito classic from 1986, although probably not as widely known as their hit Space Invaders (1978) the protagonists Bub and Bob where popular enough to be featured in a number of other games, most notably Bust a Move a,k,a, Puzzle Bubble.
This was the very first console game I owned (NES).

NES screenshot

Although the story is basically the tired old trope of "save the girl" (maybe not that tired back in the 80s) and the core mechanics are pretty simple, it does build on that mechanic to make it a truly entertaining game which require somewhat different tactics for different levels.
The two bubble dragons can shoot bubbles in which to trap enemies. The bubbles can also be used as platforms in order to get to otherwise unreachable platforms in stages.
Other bubble types are subsequently introduced as the levels progress; water bubbles, that flush away enemies, fire bubbles that burns them, and electric bubbles that stuns them.
There are also a number of bonus items. most that simply gives points, but the umbrellas are of special interest since it lets you skip a number of stages, which is a good thing considering there are 100 of them!

"In a certain village where everyone lives peacefully, Bub and Bob lived alongside their girlfriends, Betty and Patty. One day, the two girls left the village to explore the nearby woods, stumbling into a mysterious area known as the Magical Forest. Due to their unfamiliar surroundings, the two became lost, accidentally wandering into a cave deep in the forest known as the Cave of Monsters. The girls proceeded to encounter Grumple Grommit, master of the cave, who kidnapped them and trapped them on the 100th floor. Bub and Bob set out to rescue the two, but ran afoul of Grumple Grommit as well, who transformed them into Bubble Dragons. Using their newfound abilities, the two set out to journey through all 100 floors of the cave in order to rescue the girls."
(http://bubblebobble.wikia.com/wiki/Bubble_Bobble)

Arcade screenshot

The game featured multiple endings, which was rather rare at the time. I remember playing through the game only to be told I had to play it with a friend. Since I had the NES game I ended up cheating by adding player 2 at the last stage and beating it on my own. I can imagine how frustrating it was for everyone playing it in arcades, pumping the game full of money only to be told they had to do it all over again with a friend!

*minor spoiler*
In the end of course the protagonists are turned back into humans. That's something I guess the developers of the spin-offs didn't really care about.

You can get a copy of the nes game between €70 and €100 depending on the quality and whether or not it's just the cartridge.
The Amiga version goes for €200 (still in foil).
If you want a genuine arcade cabinet expect to pay closer to €2500.