What is considered a Hanukkah vessel?

The Gemara (Shabbat 23b) teaches that one who is careful regarding the lighting of the Hanukkah (in Morocco, the Menora/Hanukkiyah was known simply as “Hanukkah”), merits sons who will become Torah scholars. As such, the Rambam (Hilchot Hanukkah 4:12) writes that the mitzva of Hanuka is very dear and one should be exceedingly meticulous in lighting the Hanukkah. Rabbi Yitzhak Sagi-Nahor, the son of the Raavad, quoted by  Rabbi Avraham Azoulay (Hesed Le’Avraham, Ma’ayan 2, Nahar 58, sv. Besod Hadlakat Nerot Hanukkah) explain the Gemara’s statement as a quid pro quo; just as one is careful about all the details, laws and enhancements of lighting the Hanukkah, Hashem will give as a reward sons who will also be as diligent in all facets of the Torah.   

The Rama (O.H. 671:4) writes that the candles should be arranged in a row such that each light is discernible, rather than in a circular fashion in which all the candles contribute to the appearance of a bonfire. Furthermore, he says that one is permitted to use a candelabra in order to achieve this row-like appearance. The Mishna Berura (ibid:18), quoting the Elya Rabbah, specifies that each candle should be at least a fingerbreadth apart. 

Although strictly speaking one could simply melt a candle onto a surface and light it, Rabbi Avraham Azoulay (ibid.) recommends a stringency that each candle or wick should be placed in a vessel. According to Rabbi Avraham Bornstein (Avne Nezer, Orah Haim, § 500), one does not fulfil one’s obligation at all if one does not place the candles in a vessel because the Hanukkah lights should be reminiscent of the Menorah in the Bet Hamikdash, which itself was a vessel. One practical ramification of this ruling applies to the glass cups that many use to fill with oil and light.  Some cups are rounded at the bottom and are not able to stand on their own, while others have a flat surface and are able to stand on their own. In the laws of purity and impurity, something only attains that status of a vessel if it is able to stand on its own. Therefore, if one uses cups to light, one should attempt to use cups that are flat and sufficiently broad at the bottom. 

Summary: Ideally one should use a vessel, such as a Menora or individual cups, for the Mitzvah of the Hanukkah lights. If one uses cups, they should ideally be flat at the bottom such that they are able to stand on their own.