Is there any address monitoring application with support for multiple cryptocurrencies? This would be beneficial for all long-term investors who have many different cryptocurrencies in their portfolio and don't usually perform any transactions. Simply just to check whether your money are still there. No need to login into all your wallets, entering passwords etc. With support for many different cryptocurrencies.

I have just decided to develop such an application for my own use (it is open source, you can check it here - Cryptocheck ), but maybe there is already a good solution for this.
The best option for monitoring your accounts without logging into your wallets is to use block explorers. Blockchain data is public and block explorers are made to explore this public data: blocks, transactions, accounts, account balances. 
Here are a few:

Bitcoin, Litecoin, Dogecoin:
https://live.blockcypher.com/

Ether, ERC20 tokens:
https://etherscan.io/

WAVES, Waves assets:
https://wavesexplorer.com/

ZCash:
https://explorer.zcha.in/

Most of these block explorers also have API solutions.
I have created a playlist showing how to use the zChain ZCash block explorer API here: Zchain ZCash block explorer API - INTRO