There are many online texts of the Greek New Testament in their various editorial editions. If you need to cut and paste from an online text, all these resources are in UNICODE.
Laparola.net/greco http://www.laparola.net/greco/ has the following editions: Nestle-Aland/UBS , Westcott-Hort, Tischendorf, and the Byzantine. It also has links to many Biblical lexicons.
The Perseus Project http://www.perseus.tufts.edu/hopper/collection?collection=Perseus:collection:Greco-Roman has Westcott-Hort (scroll to the "New Testament"). It is linked to the Perseus Hopper LSJ lexicon/parser utility. The NT can be found at http://www.perseus.tufts.edu/hopper/text?doc=Perseus:text:1999.01.0155:book=Matthew:chapter=1:verse=1&redirect=true
The German Bible Society also has the Nestle-Aland Text online (as well as Rahlfs) http://www.bibelwissenschaft.de/online-bibeln/novum-testamentum-graece-na-27/lesen-im-bibeltext/
A more complete list of other sites can be found at the New Testament Gateway http://www.ntgateway.com/greek-ntgateway/greek-new-testament-texts/
The freely distributable (for non-profit) SBL Greek New testament can be found on Bible Gateway at http://www.biblegateway.com/versions/SBL-Greek-New-Testament-SBLGNT/