Will any ash catcher fit my bong?

No. It has to be the same size as your joint, male (to go into your female joint), and the same angle.

Can I use a 90° ash catcher on a slanted joint?

It will go in, but it'll lean out at the slant of the joint instead of standing straight, with its weight off to one side.

Do I need an ash catcher?

No. It's an add-on that keeps ash out of the bong, so the main part needs cleaning less often.

Ash catchers: 45° or 90°, and what fits

An ash catcher goes in where the bowl goes, and the bowl then goes into the catcher. Its joint is cut at an angle so the catcher stands up straight. So three things have to match your bong: the size, male or female (catchers are male, so your joint has to be female), and the angle.

Checking your angle

Stand the bong on a table and look at the joint from the side.

If your joint	Get a	Because
comes out at a slant	45° ash catcher	its joint is cut at the same slant, so it ends up standing straight
points straight up	90° ash catcher	its joint points straight down, into yours

You'll see 90° described two ways online: a joint that points straight up, or one that comes straight out the side. Go by the catcher: a 90° catcher's joint points straight down, so it only fits a joint that points straight up.

A lot of guides say "45 for beakers, 90 for straight tubes". That's only true when the joint is where it usually is for that shape, so check the joint itself.

The ones we have

All of these go into a female joint. You choose the angle on each one's page.

5" Monark Color Showerhead Ash Catcher $28.9914 mm male
5" Clear Showerhead Ash Catcher $29.9918 mm male
5" Spiral Color Shower Head Ash Catcher $31.9914 or 18 mm male
5" Encore Babyface Slit Ash Catcher $32.9914 mm male
5" Black Sheep Large Clear Ratchet Ash Catcher $57.4914 mm male

They're also on the 14 mm chart and the 18 mm chart, next to the bowls.

Before you buy

Size: each catcher comes in the sizes shown on its page. Check yours with a dime.
Weight: a catcher hangs off the joint. A tall one on a small, light bong makes it top-heavy.
The bowl: your bowl goes into the top of the catcher, so it has to fit that joint too. On 3 of our 5 catchers, the page shows it as "Joint the bowl goes in".

What this page doesn't cover

Wet and dry catchers (whether a catcher holds water), or how either one smokes.

Questions

Will any ash catcher fit my bong?: No. It has to be the same size as your joint, male (to go into your female joint), and the same angle.
Can I use a 90° ash catcher on a slanted joint?: It will go in, but it'll lean out at the slant of the joint instead of standing straight, with its weight off to one side.
Do I need an ash catcher?: No. It's an add-on that keeps ash out of the bong, so the main part needs cleaning less often.

Sources

Which way a 90° catcher points: Fat Buddha Glass's 90° ash catchers, "designed for bongs with upright joint placement".