It's a difficult question. Why? If I ask "How old is humanity?", I can receive a variety of answers: some will say about 35 thousand years ("behaviourally modern" humans), others 300ky (Homo sapiens), and some might even say 2 million (genus Homo).

Hinduism can be divided into multiple periods: Vedic (about 1800-600BC), Brahmanism (600-200BC, when Hinduism was first coexisting alongside Jainism and Buddhism), Classical (200BC-AD1200), Medieval (1200-1800), and Modern (1800 onward), at just a very coarse level (all of these periods can be further divided more finely). Which Hinduism do we mean? Are these all the same religion? As humans and our ancestors have evolved, making the "age question" difficult to answer, so have religions. Some religions conveniently come with a founder, providing a suitable date of origin, but even those religions evolve.

So, how old is Hinduism? The oldest vedas were probably not written down until the late 2nd millennium BC, but embody older oral traditional. Thus, about 1800BC is a reasonable date for the origin of Hinduism. We could speculatively push this further back, but we have no good evidence. The latest reasonable date we could choose would be about 1200BC (essentially saying that Hinduism came into existence when the earliest scriptures were written down).

What about other religions?

Unfortunately the history of the Avesta, the religious texts of Zoroastrianism, is not reliably known. We know that they were written down during the Sasanid Period, but we don't know if they were written down earlier. Certainly, they are of older origin, but whether earlier transmission was oral or written at any time in unknown. However, the use of Old Avestan for part of the Avesta suggests at least part of the Avesta dates back to the 2nd millennium BC. The oldest part of the Avesta appears to be the Gathas, in Old Avestan, and attributed to Zoroaster. Old Avestan is closely related to the Sanskrit of the Rig Veda (the oldest of the vedas), and the age of the Gathas can be reasonably estimated to be similar to the Rig Veda (including for both times of oral transmission before they were written down). Further, it is quite plausible (even if it is a very unpopular opinion for many) that Zoroastrianism and Hinduism grew out of an older shared Indo-Aryan religious tradition. Thus, it is quite possible (but far from certain) that Zoroastrianism and Hinduism are of similar ages. (Zoroaster is often assumed to have lived in the mid-1st millennium BC; this early dating for Zoroastrianism could mean a number of things: the usual dating of Zoroaster is out by a millennium, Zoroaster didn't compose the Gathas, or Zoroaster is a composite of more than 1 person.)

If we attempt to date Judaism to Moses, we have some immediate problems: when did Moses live, and was Moses real? Recognising that we don't have an accurate estimate, and also that the historical Moses (if there was such) might not have resembled the literary Moses closely, the mid-2nd millennium BC is possible. The Torah dates to the mid-1st millennium, but the Song of Deborah, possibly the oldest component, could easily date to the late 2nd millennium. Just as with Hinduism and Zoroastrianism, Judaism underwent major evolution. Verdict: probably over 3,000 years old, and possibly of similar age to Hinduism and Zoroastrianism.

Other major surviving religions tend to have either (a) founders of later date or (b) a lack of writings that can provide a remotely reliable date of "origin".