Is it forbidden according to the Torah to squeeze fruits and vegetables for juice on Shabbat? Since people juice almost every fruit and vegetable nowadays (e.g. smoothies), is it forbidden the same as grapes and olives are?
Rabbi Ribiat discusses this in his sefer (The 39 Melochos), starting on page 333 (vol. 2).
There are some fruits that are biblically forbidden, some that are rabbinically forbidden, and some that are allowed to be squeezed for juice.
- The biblically forbidden fruits are grapes and olives, because they are "distinguished especially for their juice."
- Rabbinically forbidden fruit are any fruits that are squeezed for their juices by a "significant segment of the population." However, he does note that there are some differences between grapes and olives and these fruits, as certain rabbinic enactments do not apply to them, as they are not forbidden to be squeezed for juice on the biblical level.
The fruits/vegetables that are allowed to be squeezed are those that are not commonly squeezed for juice. As you noted in your question
these are very few, since most fruit juices are very popular. Moreover, fruits that are not regarded as juice fruits in one country may still be Halachically classified as juice fruits if that same type of fruit is commonly made into juice in another country.
But wait! Rabbi Ribiat writes that some exceptions exist -- "[m]ost varieties of melons...are not popular anywhere for their juices and may be squeezed. These include cantaloupes, honeydew melons, and watermelons."
Please note that these halachos are subject to change, in case melons suddenly become the popular new juice fruit, or (less likely) oranges fall out of favor with juicers.
See section III of this Virtual Beit Midrash article for a more in-depth discussion of the issues at hand. (h/t Emet v'Shalom for the link)