Question:If I make a beracha on one food and then later decide to eat other foods of the same beracha, do I need to make a new beracha, or does the initial one cover them?

Answer:There are two basic halachic precedents and one major distinction for the halachot that apply here, with poskim offering differing opinions regarding in-between cases.
The Rashba and others infer from Rav Pappa’s rules (Berachot 41b) about which foods need a beracha at different stages of a meal that foods that are brought to the table during the meal are generally covered by the original beracha. This serves the Beit Yosef (Orach Chayim 206) as a source that berachot generally cover foods that were not present at the time.
The Taz (ad loc. 7) rejects this broad application, as a meal has a special ability to subsume many foods. He and the Magen Avraham (ad loc. 7) prefer the precedent of a shochet who makes a beracha before shechting several animals and then other are brought. The Tur (Yoreh Deah 19) cites several opinions as to whether a new beracha is needed: it depends if the animals are of the same species (Itur); it depends if the new animals were brought while some original animals had still not been shechted (S’mak); it depends if one had in mind to cover animals that were not yet present (Tur). The Shulchan Aruch (YD 19:7) follows the S’mak’s distinction, and the Rama (YD 19:6) follows the Itur.
Yet, in the Laws of Berachot, these pillars of halacha do not make such distinctions. The Shulchan Aruch (OC 206:5) seems to say without distinction that one does not make a beracha on the newly brought food. The Rama (ad loc.), while not necessarily arguing, says that one should preferably have in mind that the beracha goes on all the food that will be brought, and Sephardi poskim agree that this is worthwhile, considering that the Beit Yosef cites differing opinions (Yalkut Yosef 206:21).
Let us now put things in perspective. All agree that if one had in mind to eat only certain foods or amounts of the foods (e.g., those with dietary goals), the beracha is limited to that (see Shulchan Aruch, Orach Chayim 174:5). All agree that explicit intention for other foods works in all but exceptional cases. The machloket between the aforementioned Taz and Magen Avraham and the accepted reading of the Shulchan Aruch is in regard to cases where one did not give the matter thought or come to a conclusion.
Based primarily on distinctions found regarding shechita, Ashkenazi poskim say that a new beracha is needed on food upon which one did not have clear intention unless one of the following situations exists: 1) the food was before the person when he made the beracha (Mishna Berura (206:20); 2) the new food is of the exact same type as that upon which he made the beracha (ibid. 22); 3) he was not finished eating the original food when he decided to eat the new food (ibid.); 4) he sat down to eat a significant amount of this type of food (ibid.); 5) the person in question is dependent on others to determine what he will be offered to eat, e.g., a guest (Mishna Berura 179:17 – see V’zot Haberacha, p. 68).
The exceptions in which (some of) these factors do not help to exempt from a beracha include: 1) when the new food came from an unexpected place, e.g., a guest brought it after the beracha was made (Shulchan Aruch, OC 177:5); 2) if, according to the rules of order of berachot, the beracha should have been made on the second food, only explicit intention allows the first beracha to cover it (based on Rama 211:5). (For more details, see V’zot Haberacha pp. 65-67; Piskei Teshuvot 206:18).
Since the detailed halachot are hard to remember and many of them are based on machloket, it is best to follow the Rama and have clear intention to cover a wide variety of foods. If one does so on a regular basis, he should not need very clear intention each time (possibly not all agree with this – see V’zot Haberacha p. 65 – but this seems like the correct ruling).