At work, some amount of interaction is inevitable. There are some people that I just don't feel like greeting.
What is the Jewish view on this issue? What does the Halachah say about 'greeting one another', even if there is an obvious dislike?
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A Talmudic passage that may be relevant here:
מרגלא בפומיה דאביי לעולם יהא אדם ערום ביראה מענה רך משיב חמה ומרבה שלום עם אחיו ועם קרוביו ועם כל אדם ואפילו עם נכרי בשוק כדי שיהא אהוב למעלה ונחמד למטה ויהא מקובל על הבריות אמרו עליו על רבן יוחנן בן זכאי שלא הקדימו אדם שלום מעולם ואפילו נכרי בשוק
A favourite saying of Abaye was: A man should always be subtle in the fear of heaven. A soft answer turneth away wrath, and one should always strive to be on the best terms with his brethren and his relatives and with all men and even with the heathen in the street, in order that he may be beloved above and well-liked below and be acceptable to his fellow creatures. It was related of R. Johanan b. Zakkai that no man ever gave him greeting first, even a heathen in the street. (Soncino translation)
In addition to the previous answer, here are two more sources that address the topic of greeting people:
וא"ר חלבו אמר רב הונא כל שיודע בחברו שהוא רגיל ליתן לו שלום יקדים לו שלום שנאמר בקש שלום ורדפהו ואם נתן לו ולא החזיר נקרא גזלן שנאמר ואתם בערתם הכרם גזלת העני בבתיכם
Rav Chelbo said in the name of Rav Huna, Whoever knows that his friend is in the habit of greeting him should greet him first, as it is said, "Seek peace and pursue it" (Psalms 34:15). If he greeted him and he didn't respond, he is called a robber, as it is said, "And you destroyed the vineyard, the theft of the poor is in your houses" (Isaiah 3:14).
(The second statement is playing on the dual meaning of עני as either "poor person" or "response," according to the commentary of Ya'avetz.)
This source explicitly recommends greeting first those who are in the habit of greeting you.
Regarding greeting idolaters (which seems to be a concern you had from your comment): The Mishnah Gittin 5:9 also says ושואלין בשלומן מפני דרכי שלום, "We greet [gentiles] for the sake of peace." The Gemara 62a says that the case is greeting an idolater on an idolatrous holiday: "A person shouldn't enter an idolater's house on his holiday to greet him, but if he found him in the market he greets him weakly and seriously. It further brings a statement in the name of Rav not to greet an idolater twice. Neither statement implies that there is any problem with greeting an idolater in general on days other than holidays.
Here are two more relevant sources from Pirkei Avot
Shammai says, "Make your Torah fixed, say little and do much, and greet (receive) every person with a pleasant countenance."
Rabbi Matya the son of Charash would say: Be first to greet every man. Be a tail to lions, rather than a head to foxes.