BibleGateway has become almost a de facto standard on Christianity.SE. They also have the following Greek texts:
- 1550 Stephanus New Testament
- 1881 Westcott-Hort New Testament
- 1894 Scrivener New Testament
- SBL Greek New Testament
For Hebrew, there's The Westminster Leningrad Codex. There's also the Vulgate, which might be relevant for some questions.
I don't know how useful these texts are (I'm not a scholar). One reason for wanting to use BibleGateway might be that there's a ready-made userscript for generating MarkDownready-made userscript for generating MarkDown suitable to be used on StackExchange sites. It doesn't work for Hebrew, unfortunately; I'll look at fixing that if people show interest. For Greek, it should work nicely; example output:
16 Οὕτως γὰρ ἠγάπησεν ὁ θεὸς τὸν κόσμον ὥστε τὸν υἱὸν τὸν μονογενῆ ἔδωκεν, ἵνα πᾶς ὁ πιστεύων εἰς αὐτὸν μὴ ἀπόληται ἀλλὰ ἔχῃ ζωὴν αἰώνιον. 17 οὐ γὰρ ἀπέστειλεν ὁ θεὸς τὸν υἱὸν εἰς τὸν κόσμον ἵνα κρίνῃ τὸν κόσμον, ἀλλ’ ἵνα σωθῇ ὁ κόσμος δι’ αὐτοῦ.