HTTPS uses SSL encryption to protect the data packets in transit. The IP addresses are visible so that the ISP can log "flow" - the source, destination and rate of data, and will divulge that to law enforcement if presented with a court order or legal document. Many websites (Facebook, Google ...) use SSL now even for basic navigation, and almost always for logins and for sensitive transaction (shopping, banking etc)
TOR encrypts all traffic and sends it via a number of randomly chosen nodes to a random exit node, often in a different country. The ISP can see that you are sending a quantity of data, but cannot tell the ultimate destination. The unpredictability of the exit node makes it unreliable for avoiding country-based blocks.
The Tor browser is configured to use the Tor network for traffic. In the most common configuration, other programs such as the Flash plugin or bittorrent will continue to use the original IP address, risking exposure if a remote website can correlate Tor web requests with Flash media requests.
A professional secure VPN (e.g. Cisco, Junos Pulse) encrypts all traffic between a client and a trusted network, such as an employer's network. The client is assigned an IP address on the remote network (hence the name Virtual Private Network). The ISP can see the amount of traffic, and the fact that it is going to a VPN server, but not any of the content. This is a preferred solution for a commercial traveller, where they trust their employer but perhaps not a hotel or airport network connection.
A "free" VPN is probably not a good solution for anyone. Some force otherwise encrypted connections to be insecure, and then insert adverts into web pages.
According to a recent story (May 2015) Hola sold user's bandwidth for botnets.
An ISP could in theory see inside unencrypted VPN traffic to see the real destinations, while the VPN operator could do the same, even if it was encrypted. Users are thus declaring that they trust the VPN operator more than they trust their ISP. Since the ISP usually operates under the laws of the user's jurisdiction, and the VPN does not, I wonder just what the point is.
A Web proxy is a solution which proxies just Web traffic. The client keeps its original IP address, while the web browser is configured to use a proxy to pass HTTP requests.
Some "free proxy" sites are actually lists of compromised or badly configured hosts, rather than lists of properly configured proxies. The real operators of such sites may well log everything and possibly publish it or pass it to law enforcement as evidence of an attack on their network. (I have seen such as site on one of these lists).
This is not to say that there are no trustworthy commercial VPNs, whom you can pay for a secure connection via an endpoint in another country. But I do not myself know any.
Written 1 Jul