Avraham is labelled a "Prince" as the first Convert: Succah 49b
Converts have a special bond of love for each other: Pesachim 113b
We learn what a convert must do for conversion from what the Jews did before they received the Torah at Mount Sinai: Keritot 9a
How we know that we accept converts even in an era when there is no Beit haMikdash in which to bring a conversion offering: Keritot 9a
The Mazal of Converts was present at the Giving of the Torah: Shabbat 146a
Converts are like boils, if they mislead others with incorrect learning: Yevamot 109b [according to Rashi]
Converts are like boils, if they aren't serious: Yevamot 109b [accoding to Tosafot]; Niddah 13b
If a Convert is serious, he must be accepted: Tos. Yevamot 109b #3
[Non-serious] converts delay the arrival of the Mashiach: Niddah 13b
Converting in order to marry: Menachot 44a
Concern lest people think one converted for the sake of financial gain: Bava Metzia 72a