There are five general ways to use Gmail, every one has it's own advantages.

1. Web Gmail

Accessing Gmail via the webinterface is what most people do, It's where most of the powers of Gmail are accessible. Sometimes however it might fall a bit short. 

Advantages

• Easy to search
• Possibility to set up filters 
• Messages are saved on server 
• Access to Gmails contacts-database 

Disadvantages 

• Messages are kept on server 
• Not possible to sort
• Requires constant internet connection
  

2. POP Gmail

When accessing your gmail-account via POP you use a third-party (non-google) email client to download the messages from your Gmail account 

Advantages

• Use almost ANY third-party email application.
• Not required to be constantly connected to the internet. 
• Possible to keep you'r own backup of emails 
• Downloads one copy of every mail in your inbox. 

Disadvantages

• You don't have use of Gmails contact-database
• You cannot set up server-side filters via POP (you can however set them up via the web-interface)
• Only gets one copy of the mails in your inbox (if you've downloaded it on another client, you won't get it again in the next client)
  

3. POP recent Gmail

If you, in you connection settings for you POP-gmail account puts a "recent:" before your email-adress, you will instead of donwloading every message once, download every message from the last 30 days.

Advantages

• Get the same messages to multiple clients.

Disadvantages 

• If you choose to delete messages from the server in the client (or did not explicitly say to leave them on the server), they will be moved into the trash-folder after you've fetched them.
• Only fetches the last 30 days worth of emails in your inbox.
  

4. IMAP Gmail 

When using the IMAP-protocol you will only download what you're after for now. It's great for mobile users, where every bit of data is costly. It works as that you only first downloads the headers of an email. When you open the email, you download the message body, and the headers of the attachments. When opening the attachments, you download attachments. 

Advantages

• Saves data
• You can archive, and label messages from within your email client
• See all your emails
• You only download what you need for the moment, and thus saving transfer-data 

Disadvantages 

• Not all email clients support IMAP (although most do)
• If you have many messages, your email client may take a long time to synchronize with the server
• Unless you configure your client to download all messages, you won't get a complete backup copy of all your mail like you do on a POP client
  

 5. Gmail Mobile

See the Gmail help center for options on how to access gmail from your mobile device.