Several examples of halachah that has actually changed during the past 1500 years:
In talmudic times, blind men could not receive aliyot or count for a minyan. Today, they do both.
In talmudic times, a bridegroom was exempt from reciting the shema on his wedding night. That is not the case today.
Women used to be able to read the megillah for a man. The Rema accepted an opinion and almost all Ashkenazic poskim follow him. (Rabbi Ovadiah Yosef does not accept the Rema on this.)
Chazal prohibited the use of flammable material to wipe excrement off ones body. Today, we use toilet paper.
There have also been real changes in how we treat and relate to non-Jews; it is possible to say that the non-Jews of today are not like the non-Jews of talmidic times so this may not be a halachic change but a change in classification.
—
However, there aren’t very many examples of actual halachic changes. What does change is custom (minhag), and it can often change quite dramatically. For example, our siddur has many post-Chazal additions including the texts for selichot, tachanun, and parts of pesukei d’zimra, piyutim, Kabalat Shabat, kinot for Tisha B’Av, and the entire Simchat Torah sidur. Furthermore, many Ashkenazic Jews dropped their former Nusach and adopted Nusach Sfard or Nusach Ari.
Another example is the term “rabbi” which had a very different meaning in talmudic times than it does today. Chazal would have never imagined internet semichah programs!
Yet another example is the unprecedented level of formal Jewish education that is now available to Jewish women, even including formal talmud study. Almost every single Modern Orthodox community in the world today now teaches at least some T”S”B”P to women. Rambam would never have imagined that.
The lesson I see from Jewish history is that change that does not contradict halachah can often be accepted, but that change that requires changing halachah is almost never accepted.
edited