Symbols for Quantifiers Other Than $\forall$ and $\exists$

The most commonly used symbols to express "for all but finitely many" and "there are infinitely many" are $\forall^\infty$ and $\exists^\infty$, respectively.

Not quite a symbol per se, but of course there is "a.e." ("almost everywhere"): "for all but a set of measure zero". Probabilists call it "a.s." ("almost surely"). They are also in the habit of writing "a.a." ("almost all"): "for all but finitely many" and "i.o." ("infinitely often"): "for infinitely many".

In potential theory, one also sees "q.e." ("quasi-everywhere"): "for all but a set of capacity zero".

Jaśkowski used $\Pi$ for quantifying over propositions. So he would write

$$\Pi a . \Pi b. a \to b \to a$$

It is useful for formalizing things like "does double negation elimination imply LEM", which you have to write as

$$(\Pi a. \lnot \lnot a \to a) \to (b \lor \lnot b)$$

IIRC he used $\Sigma$ for existential quantification over propositions.