In much of Ulster, when the "native" Irish learned English (which mostly occurred after the Plantation), they frequently learned it from Scots-speaking settlers (some of whom were, however, still Gaelic speakers). That explains the very different, obviously Scottish-influenced accents one finds in Ulster, as compared with the rest of Ireland. The process of learning English was so heavily Scots-influenced that I've read that the Irish natives referred to learning English as "lifting the Scots".
Wikipedia has a very informative article about Scots, discussing how it developed, spread, and was ultimately replaced by more "standard" English (in most places, anyway). Although it is mostly focused on the history in Scotland proper, it does mention the use of it in Northern Ireland:
http://en.wikipedia.org/wiki/Scots_languageEditing to say that Wikipedia also has a separate, very interesting article on the spread of the Scots language to Ulster, with maps and all:
http://en.wikipedia.org/wiki/Ulster_Scots_dialects