A great many people assume that Easter was originally a pagan holiday, and that many of the customs associated with it were originally pagan customs. This is not wholly implausible, as Christians would occasionally convert pagan holidays and customs. But in this case, there is not only a complete lack of evidence for it, there is plenty of evidence against it.
In most languages, the Feast of the Resurrection is known by some variation of Anastasia, the Greek word for Resurrection, or Pascha, the Greek form of the Aramaic word for Passover, and this is of course the actual origin of Easter as a holiday: it was a celebration of the resurrection of Christ based on the Jewish Passover, taking into account that Christians stopped using the Jewish calendar. The holiday is not based on any prior Greek or Roman holiday.
Languages heavily influenced by Old English, including, of course, English itself, use the word 'Easter'. This is a peculiarity that would be impossible to explain at all except that one relatively early authority gives us an explanation that seems plausible. St. Beda, also known as the Venerable Bede, tells us that the name comes from one Anglo-Saxon name for a month, roughly about April, Eosturmonath, which was named after a goddess, Eostre, who had some holidays during that period. Given that Bede is quite careful, we can be reasonable sure that this was in fact said by some people in his day; he's also not likely to be wrong about there having been such an Old English word for the month, particularly given that it fits linguistic evidence elsewhere. But we don't actually even know for sure that there was really a goddess named Eostre or whether people in Bede's time (the late seventh century, by which time the English were fully Christianized) just knew the name of the Easter season came from an old word for the month and inferred that the month was named after a goddess. Bede is our only authority, as Eostre is mentioned nowhere else at all; there is not a trace of her worship, if it existed, except in the name. The name 'Eostre' has possible cognates in some Germannic personal and place names that may possibly refer to a goddess of the dawn, and there are a number of inscriptions on the continent a couple of centuries before Bede to goddesses known as Matronae Austriahenae, who may possibly be related. Except for Bede's testimony, all of the reason for thinking there was even such a goddess is based on linguistic analogies and etymological inferences, which may or may not be any good.
As we learn nothing about the goddess from Bede except her name, the name of the spring month, and that she had some feasts in her honor at that time, and analogy tells us nothing but that she might possibly have had some association with the dawn at some time, we know nothing about the rites used to worship her, which, if like other minor gods and goddesses, in any case probably varied a lot from place to place. That the association of Easter with rabbits and hares has to do with the goddess is completely a guess based on the assumption, which may or may not be true, that a spring-worshipped goddess must be a fertility goddess; it's certainly true that rabbits and hares sometimes figured in various rites in the ancient world. But in reality, the first actual evidence of anything like a cultural bunny-association with Easter seems to be in post-medieval Germany. The Easter Bunny itself, of course, is a primarily American invention (although possibly Britain actually originated the first versions), based loosely on customs of German immigrants. We have likewise no reason to think that eggs were associated with Eostre; the probable reason for their association with the holiday was that medieval peasants would usually fast from eggs as well as milk and meat for Lent, so of course being able to eat eggs again would be an easy, and relatively cheap, way to mark the day. Conceivably a similar explanation applies to rabbits.
Major holidays are powerful attractors. We see this most forcefully with Christmas, which has managed to absorb independent customs originally associated with all the lesser holidays around it: St. Nicholas's day, St. Lucy's Day, St. Stephen's Day, Epiphany, including Winter Solstice customs, some of which likely go back to pagan times. But, of course, it's always operative; Halloween slowly absorbs every October custom, Thanksgiving in the United States slowly absorbs every November custom, etc. It would not be at all surprising if Easter, the single most important holiday in the Christian calendar, managed to absorb customs previously associated with other spring holidays in its long centuries of dominance, and there are occasional plausible examples of this. But Easter is Easter, and not some other thing.
