you can just use JSON-RPC
https://en.bitcoin.it/wiki/API_reference_(JSON-RPC)#PHP
https://en.bitcoin.it/wiki/Original_Bitcoin_client/API_calls_list
pretty easy to work with: just install bitcoin core, let it sync and call the API directly
Awesome, I knew there has to be something like this. Looks like exactly what I am looking for, thanks!
Still: Is there some public API service or something that just allows you to call few basic commands? What you've posted is great, but may be a little overkill for what I actually need, but I might to learn to use it anyway. Any other suggestions anyone?
If i'm not mistaking, blockchain.info also has an api for which you don't need an api key, if i remember correctly, it's limited since it only allows x calls every 24 hours.
https://blockchain.info/api/json_rpc_api
The big plus for this api is that it is fully compatible with the original Bitcoind RPC protocol, so if you develop code and use this API, you should be able to switch to the bitcoind api without to much troubles.
If you just want a block explorer, you can also have a look at the insight api, i hear it's easy to use and install, but in essence, you're running a full node.