As a regular user you might not care much if the proxy you are using is transparent, anonymous or elite. Maybe you prefer to pick “elite” just because of the name, but that’s it.
So what are the differences?
A proxy can send three different headers:
REMOTE_ADDR HTTP_X_FORWARDED_FOR HTTP_VIA
REMOTE_ADDR always sends the IP address of the proxy server. It would also be sent if you were just browsing regularly.
A transparent proxy sends your real IP address in the HTTP_X_FORWARDED_FOR header, this means a website that does not only determine your REMOTE_ADDR but also check for specific proxy headers will still know your real IP address.
The HTTP_VIA header is also sent, revealing that you are using a proxy server.
An anonymous proxy does not send your real IP address in the HTTP_X_FORWARDED_FOR header, instead it submits the IP address of the proxy or is just blank.
The HTTP_VIA header is sent like with a transparent proxy, also revealing that you are using a proxy server.
An elite proxy does only send the REMOTE_ADDR header, the other headers are blank/empty, hence making you seem like a regular internet user who is not using a proxy at all.
This technically seems to be against some RFC guidelines regarding proxy servers, but it seems like no one cares. 
Keep in mind that there *may* still be possibilities to detect the proxy, to prevent being detected do not use a proxy server with the standard ports (8080,3128, 8888, 1080,..) and if possible one that requires authorization.
There are several more things that can identify you, such as javascript, flash,..
To check how anonymous you are, use the following website: http://whoer.net/ext
Now are transparent and anonymous proxies useless? Technically, yes.I am not aware of if an elite proxy produces any higher server load than a transparent proxy.
Sometimes internet providers offer transparent proxy servers for their customers to speed up the loading time of websites (proxy servers can cache websites and deliver them faster). As anonymity is not a desired effect they are just transparent.
As the internet is getting smarter, transparent proxy servers stop working to bypass restrictions. Certain one click hosters like share-online.biz block proxy servers, you need an elite proxy to download from there using the free method.
Also transparent proxy servers do not seem to work any longer on youtube, which pretty much lowers the usefulness of a transparent proxy server a lot.
However you can still use them for most sites and to bypass restrictions at school.
An anonymous proxy server does not tell websites your real IP address anymore. This can be helpful to just keep your privacy on the internet. The website can still see you are using a proxy server, but in the end it does not really matter as long as the proxy server does not disclose your real IP address. If someone really wants to restrict page access however, an anonymous proxy server will be detected and blocked.
An elite proxy server is ideal to pass any restrictions on the internet and to protect your privacy to the fullest extent. You seem like a regular internet user who lives in the country that your proxy server is running in.
If you have your own virtual private server (VPS) and would like to set up a proxy server, an elite proxy is probably the way to go.
If you do not have your own server but have to rely on public proxy servers you should carefully select one depending on what you need. Transparent proxy servers are mostly a lot less overloaded than elite proxy servers. Especially the elite proxy servers from large websites like hidemyass.com become horribly slow within seconds after being published.
The next step to be even more anonymous would be to use a Virtual Private Network (VPN) which also encrypts the traffic between you and the server. They are not as easy to install or use though, and paying for a VPN service in my opinion costs more than what it’s worth. Furthermore services like hidemyass.com will also quickly disclose your identity if there’s only a slight hint of a court order. Using a public elite proxy might grant you more anonymity in this case.