The Avnei Nezer (Siman 500) discusses whether one needs to use a kli to light the menorah. The Chessed L'Avraham brings down 15 madreigos of a menorah, the best being gold then silver, copper etc. He then writes that one can not use egg shells because it is not a kli and also you can't use a kli that can't support itself. The Avnei Nezer paskens like the Chesed L'Avraham. He tries to prove that in the Beis HaMikdash, the kli used to hold the oil was considered a chelek of the ner of teh menorah and therefore, by Chanuka as well one needs a kli to hold the oil.
There are several chumros that come out of this.
1) One can not use a hollowed out potato to hold the oil since food is not m'kabeil tumah and is not considered a kli. (l'fi zeh tzarich iyun on the Holocaust stories where they were moser nefesh to put oil in a potato and light it. Acc. to the Avnei Nezer they were not yotzei).
2) If the kli can't stand by itself it is not a kli. Rav Shternbuch (Teshuvos V'hanhagos chelek 2) also paskens like the Avnei Nezer and he says that most of the glass cups we use are no good. Most of the cups we use have a nipple on the bottom and they can't stand on their own. Accordingly, they would not be considered a kli and you would not be yotzei ner chanuka.
3) If one has a gold menorah but uses glass cups, you would lose the hiddur of using a gold menorah, since you are really lighting with the glass.
4) If you just stuck candles down on the table you would not be yotzei.
Other than the Avnei Nezer and Rav Shternbuch, the other poskim I saw are all meikil for different reasons.
1) The Shevet Levi argues on the whole dimyon to the menorah in the Beis HaMikdash. Even if the Avnei Nezer is correct that in the Beis HaMikdash the kli is a chelek of the ner, who says that we would say teh same by the Chanuka menorah. The menorah in the Mikdash could not be made out of wood and only had 7 branches, while our menoros can be made out of wood and have 8 branches.
2) Rav Shlomo Zalman Aurbach zt"l in Halichos Shlomo says that the glass cup is batul to the menorah. Therefore, as long as the menorah can stand by itself, it makes no difference if teh glass cup can stand by itself. Furthermore, if the menorah is gold, you would still get the hiddur of using a gold menorah.
3) The Sdei Chemed (Mareches Chanuka Os 7) says that if the kli was originally made so that it couldn't stand it si not a chisaron in the kli and it is still considered a kli. The rayah is from a mishna in keilim. I also saw this brought down in a sefer on Hilchos Chanuka and the comparison was made to nitilas yadayim. By nitilas yadayim, we pasken if the cupo can't stand on its own but it was made liek that , it is still a kli. So hu hadin by Chanuka. Rav Shternbuch mentions this dimyon but he rejects it. I don't understand his sevara for rejecting it, but ayin sham.
4) The Az Nidbiru (chelek 13 Siman 49) points out that the Avnei Nezer brings Rishonim who are choleik on teh Chesed L'Avraham, namely the Radvaz, the Rashba and the Ran. Also, the poskim never indicate we should be machmir like the Chesed L'Avraham.
5) The Chacham Tzvi writes that one is yotzei if you stick candles on the wall. We see he didn't require a kli.
6) Finally, the Az Nidbiru (chelek 13 Siman 49) has a totally different understanding of the Chesed L'Avraham. When the Chesed L'Avraham writes that the kli must stand by itself, that is only because otherwise there won't be enough oil b'zman hadlaka to last the shiur.