Is it illegal to sell something on craigslist without adding a regions value added tax? Say for example GST is 10%, and I sell my bike for $100; do I technically have to charge $110, and send $10 to the government?
In the U.S.: To my knowledge all states and jurisdictions that with a "sales tax" technically have a "use" tax, which means the tax liability falls on the purchaser. However, they require "businesses" (whose exact definition varies by jurisdiction) to collect and remit that tax on behalf of "consumers" (which can also vary, e.g., to exclude businesses that resell).
Historically consumers have avoided paying use taxes by purchasing from out-of-state businesses that are not subject to their home states' laws on withholding the use tax: while technically a violation of the tax law neither consumers nor states have had an interest in calculating or auditing use taxes owed, except in the case of very large and unusual transactions.
There is a large effort underway by states and "brick-and-mortar" stores that lose business to this virtual "mail order tax exemption" to subject out-of-state businesses to the requirement of collecting use taxes on behalf of the state. A few online businesses (notably Amazon) have acquiesced to this demand.
To answer your question: In the U.S., an individual who is not making a "business" of selling items or services is generally exempt from the requirement to collect sales tax. It is the purchaser who has the legal obligation to declare and pay tax on such transactions. But purchasers rarely do.