Short answer: connected with = a relationship between two parties (e.g., people, company) connected to = a physical or signal-related connection (A is connected to B; my computer is connected to the Internet) Answers above are good also.

With "be" as you have it, "connected" is being used as an adjective (or arguably as a participle in a passive construction), and in that case, I think "connected with" is not usual. Things are either connected (no preposition) -- e.g. "these cities are connected by highways", or you might say "connected to" (e.g. "the printer is connected to the network"). However, as an active, intransitive verb, you do come across "connect with", and it means something like to have or establish an affinity, e.g. "I met his parents last night and I really connected with his mother".

Normally, you "connect with" a person or an idea. For example, " I really connected with Bob last night at dinner," or "I connected what she was saying about global warming." It usually means you have something in common. "Connect to" refers more to things like, "I connected to the wifi".