Depends on the type of party whether you'd expect to be fine bring friends. If it's more of a small gathering then I'd only ask to bring a friend if they were like visiting and staying with me, I wouldn't expect many to be asking to bring friends. If it's a proper party then I'd consider bring friends normal.
I've hosted a few big parties and I'd assume people I know well might bring a friend or two, if they want to bring more then I'd expect them to ask and I'd say yes to at least the first few. People I'd invited but don't know particularly well I'd expect to always ask and may or may not say yes depending on numbers. After that I'd probably start being more choosy and only saying yes if they are people I kind of know but I'd still think it's fine to ask, it's much better than not asking. On the night I'd still always end up with a few people texting asking if they can bring friends, I guess they just happened to end up with them, and if there was still space to move I'd say yes. I did once have someone text at 2-3am asking to bring 7 friends, that was taking the piss.
I think part of the fun is the new people you don't really know but are all right because they are friends of friends. It makes for a more interesting night. Remember not everyone who says yes will turn up anyway.