Will sharing slow down my Internet connection?

Yes. Sharing resources does cause slower individual access. However, whether the slowdown is noticeable depends on many factors.

If you share a high-speed broadband internet connection you will very rarely notice additional computers, simply because they're not consuming the entire bandwidth, and even if they do, it is often for a couple of seconds. Also, many web sites serve pages slower than your broadband connection can handle due to their load, internet congestion, etc. You would only see a noticeable slowdown if you're hosting some type of servers, such as P2P programs, or maxed out game servers.

In addition, note that using hardware routers is a much more efficient way to share your internet connection than using software (making your computer act as a server to other computers on your LAN).