Although there's already a very good accepted answer, I would like to add some information that might help people understand why things work the way they work.
Contracts are simply wills of parties coming together in agreement. For as long as there are parties who wish something and these wishes come together as an agreement, there is a contract. This is generally true, regardless of jurisdiction, and scope. This is because contracts have meaning even outside the legal framework. Which leads us to contract law.
Contract law is in fact a contract as well. The contract law contract came as an agreed will of the members of a community (parties) to have means of enforcing contracts.
Enforcement of contracts is a completely different concept from the contracts themselves. In contract law, the community agrees what they wish to enforce by taking into consideration a wide range of aspects like impact and practical enforceability, and that's why a real-estate contract usually has to be in written form, maybe even notarized, while supermarket transactions only require verbal, or even non-verbal non-written contracts.
On top of contract law, there are usually a lot of other contracts (laws) that delegates enforcement of lower level laws. These are the civil code, penal code, etc in civil law countries, and also court-cases in UK and a few of their former colonies.
Since the entire legal system is a contract, it follows that contracts are requirements for the existence of legal systems, and not the other way around. The most important aspect of all of the above is that contracts transcend legal systems. Enforcement of contracts though doesn't and it is defined within a legal system as a contractual clause.
All contracts are binding, as long as they are indeed contracts. The law provides guiding for what is not a contract, in order to prevent useless lawsuits. E.g. if I say in a pub "I bet Liverpool is going to win this year" and someone in the bar nodes, it's just a way of expressing my feelings about Liverpool's game play, without any obligations on my side to actually bet, hence not-a-contract. Similarly, jokes are not contracts, swears are not contracts (FU doesn't bind me to anything, even if you agree).
So, all contracts that are indeed contracts are binding, but only some are enforceable (as stipulated by law), and out of those, only some are easy to enforce (written notarized contracts).