The only "obvious" convert mentioned in the Bible that I can think of is Ruth. I am looking for a list of converts mentioned in the Bible as well as those named in the Mishna and Gemarrah. Is there such a consolidated list?
Wikipedia, as mentioned in the comments, brings a partial list of Tanach figures:
Bnei Avdei Shlomo
Ovadiah the prophet
Rachav (likely her family as well)
Shimrit the Moabite
To these I'll add:
Bityah, daughter of Pharaoh
Shim'at the Amonite
The Amalekite ger
Yarcha the Egyptian ex-slave
The foreign wives of King Shlomo
Izevel (most likely2)
Bnei Rechav (according to some views)
Do'eg the Edomite (according to some views)
Uriah the Chitite (according to some views)
Ma'acha, daughter of Talmai king of Geshur, wife of David and mother of Avshalom and Tamar
Na'aman (according to some views)
I think that's it.
Wikipedia also brings a list of Mishnah/Gemara gers:
Aqilas the ger
K'ti'ah bar Shalum
To these I'll add:
Descendants of Haman
Descendants of Sisra
Descendants of Sancheriv3
The Roman general Neron Caesar
The parents or ancestors of Rabbi Akiva
The three converts who came to Hillel
The wife of Turnus Rufus4
Baitos, brother of Munbaz, son of Talmai
Yehudah the Amonite ger (Yadaim 4:4)
There may be more, though.
1 I assume this is based on the opinion that the Alshech on Ruth brings, that Machlon and Chelyon not only held that Moabite women could be converted, but a beit din of two was enough (after Elimelech died, they were only two Jewish men in S'deh Moav) and proceeded to convert both Ruth and Orpah, and what happened subsequently in Beit Lechem was a need to re-convert Ruth because the halacha hadn't been agreed upon yet.
2 Recently I saw somewhere (don't remember where, unfortunately), that though it doesn't ever say explicitly that she was the mother of Achav's children, she is the most likely candidate for a number of reasons, the main one being that no other wives of Achav are mentioned. For more info, see here and here.
3 Though these might only include Shma'ayah and Avtalyon.
Just one more to add to @Harel13's very comprehensive list.
Shua the wife of Yehuda.
It says in Bereishis 38:2:
וַיַּרְא־שָׁ֧ם יְהוּדָ֛ה בַּת־אִ֥ישׁ כְּנַעֲנִ֖י וּשְׁמ֣וֹ שׁ֑וּעַ וַיִּקָּחֶ֖הָ וַיָּבֹ֥א אֵלֶֽיהָ׃
There Judah saw the daughter of a certain Canaanite whose name was Shua, and he married her and cohabited with her.
Targum Yonasan there writes:
וַחֲמָא תַמָן יְהוּדָה בְּרַת גְבַר תַּגָר וּשְׁמֵיהּ שׁוּעַ וְגַיְירָהּ וְעַל לְוָתָהּ
That Yehuda saw there the daughter of a merchant man whose name was Shua, and he proselyted her, and entered with her.