Moog Grandmother, and probably Matriarch as well.
Sequential Pro One
Toraiz AS-1.
Not certain about this, but I think Volcas/SQ-1
OB-6, Prophet 6, Prophet Rev 2.
I’ve been interested in this topic too.
SH01A
KORG MONOLOGUE/MINILOGUE (?)
Microbrute
Moog Grandmother
…
KEYSTEP + ANY SYNTH
0ctrl + any semi modular synth
…
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lol I own two of those and didn’t even realize this 
I don’t use the sequencers on them often, really.
I was just gonna say SQ-1. if the OP is looking to do the trick where you program a sequence and then start to send it an odd clock (like not just straight 8th or 16th gates), if you have an SQ-1 you can do that with pretty much anything.
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Didn’t realize the keystep could do this, which is a bonus (as I have 1). Also, the SQ1 is a cheap option, so thanks.
And yes, that’s the exact trick I’m looking to do 
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it’s a classic. and great fun!
There’s also the TB-03 and the DFAM that I can think of.
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Korg Monotribe.
Evolver
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Does anyone know if the microfreak is capable of this?
OP-1’s endless sequencer
Are you wanting to use an external trigger? Or do you mean simply the “trigger” generated by a keypress? I don’t think I’ve ever used an external trigger but that could be quite fun. I do very much love step advance from the keyboard. Happy accidents abound!
Using an external trigger/clock to advance the sequencer a step. This way you can create a sequence on the synth and then use the trigger/clock input to play it with an interesting rhythm.
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System 8 hasn’t been mentioned yet. Only the sequencer though, not the arp.
a great example:
the Drumatix is sending the rimshot trigger to the SH-101 clock input to advance the sequencer. otherwise, the SH-101 would be using the LFO to clock the sequencer.
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Moog Mother 32.
Roland JX-3P.