Geth
The Ethereum implementation in the language Go is more or less the official client of Ethereum. Nearly 20,000 Geth Nodes are the backbone of the Ethereum network. When the Ethereum developers agree on new features, they are usually found first in Geth, and Geth's code defines the consensus of Ethereum.
However, Geth requires relatively much computing power, and it takes very long before Geth has loaded the entire blockchain. https://geth.ethereum.org/
Parity
The second most popular client of Ethereum, Parity, is written in the programming language Rust. Compared to Geth, Parity impresses with a much better performance. If you start Parity, you will notice that the client requires a lot of computing power. But Parity is ready for use in just a few minutes. This is due to the -warp mode, which parity uses the other parity nodes to build the state. By default, Parity runs in Light mode, which limits the need for hard disk space. https://parity.io/
MyEtherWallet (MEW)
Actually, MyEtherWallet is an online wallet. MEW also supports the most common tokens on ethereum basis.
If you do not want to run your wallet on a foreign server, MEW can make the function "available offline" in the browser. Since MEW works independently from the server, you can also use the wallet locally, like similar wallets for Bitcoin. This combination of ease-of-use, independence from a third party, and relatively broad functions makes MEW the most popular Ethereum wallet. https://www.myetherwallet.com/
Metamask
Metamask is a plugin for the Chrome browser. It brings a minimalist wallet into the browser, with which you can receive and send ethers and some tokens. The wallet is very simple, but fulfills the basic functions. The developers have been planning for quite some time to offer the Wallet also for Firefox and other browsers, but so far it only works with Chrome. https://metamask.io/
Many users prefer hardware wallets to store their tokens securely. All current hardware wallets now support Ethereum. Most popular is the Ethereum app from Ledger. https://www.ledgerwallet.com/
But also Trezor has made many friends in the Ethereum scene with the integration of the backend of MyEtherWallet. https://trezor.io/
Jaxx
There should be no wallet that supports as many coins as Jaxx. Besides Bitcoin and Ethereum, you can also use Dash, Ethereum Classic, Zcash, Litecoin and more with Jaxx. Also some ERC20 token - like REP from Augur - work with Jaxx.
Jaxx runs on Windows, Linux and iOS, on computers, tablets and smartphones, as well as in the browser. For many, Jaxx is the most convenient wallet to store Ethereum on the smartphone. https://jaxx.io/
Exodus
The second largest multicoin wallet is exodus. In addition to Bitcoin, Ethereum, Dash and Litecoin, Exodus also supports a large number of tokens based on Ethereum: BAT, Augur, EOS, OmiseGO, Qtum and more. This is likely to make Exodus extremely attractive to many ICO fans.
Exodus also convinces with a relatively simple and transparent key management as well as good optics. But the downside is that not all parts of the Wallet software are open source and that Exodus runs only on the PC. https://www.exodus.io/
Ethaddress
With the Seeds of Ledger, Trezor, Exodus and Jaxx as well as with MyEtherWallet one can build relatively simply a Paperwallet. However, there is also a page that is specifically designed to form Ethereum paperwallets. For me the site has not worked, either online or offline. But maybe you're more lucky. http://www.ethaddress.org/
imToken
ImToken is probably the first Ethereum wallet for Android and iOS. It was written by the Chinese Ethereum developers of ConsensLab and is, unfortunately, not completely open source. However, inToken convinces through the integration of a multitude of tokens, a seed as well as the possibility of multisig wallets. https://token.im/
Xeth
Perhaps the most promising project in development is Xeth. Xeth uses the decentralized namespace BitProfile and allows it to receive ethers without ethernet addresses. In addition, Xeth allows stealth addresses for Ethereum. http://xeth.org/
LETH
Leth is a still experimental mobile ethereum wallet. It is currently running in the Testnet and the developers do not recommend using it for larger amounts. Leth promises an exceptionally broad range of options for a mobile wallet, which may include the management of various tokens as well as the interaction with other smart contracts. https://www.inzhoop.com/