iTunes lets you view your listings of songs, movies, TV shows... in three different ways: List view, Grid view (which replaces the old Album view), and Cover Flow. The View you choose only affects the appearance of the listings: options like sorting and filtering are still available. With the latest versions of iTunes, views have increasingly added useful features. You will most likely switch between views, rather than stick to a favorite one, based on what you are trying to achieve at a particular moment. The Views button is displayed on the left of the search field in iTunes' main window.
iTunes List View
iTunes' List View is the simplest view: it displays a text only version of your current listing. This view is faster on most computers, since it involves no graphics; scrolling fast with graphics causes delays with many older video cards. Note that using List view in iTunes does not affect the visibility of album artwork.
To display your songs in List View, go to View > List View or click the List View button. List view is the most compact way to look at your music in iTunes, and allows you to quickly sort your music any way you want, simply by clicking on the appropriate column header (clicking again will invert the sort, and list view will display the content in ascending order).
Keyboard shortcut: press Ctrl+Alt+3 (Windows) or Option+Command+3 (Mac) to use List View in iTunes.
iTunes Album View - (has been removed from latest iTunes: see Grid View)
iTunes' Album View lists the same information as List View, but also includes a snapshot of the artwork associated with each item or group of item. Unless songs (or movies, TV shows...) are sorted by Album, this view can be rather inefficient, and require a lot of vertical scrolling, since each entry is at least as high as the artwork and album information displayed. Album View is possibly the closest to a real world CD collection you get in iTunes.
To display your music in Album View, choose Album View from iTunes' View menu. Tutorial Update: the latest version of iTunes did away with Album View, and has replaced it with "Grid View" - you can mimic the former Album View by using List View, and toggling the visibility of the album artwork column,
as shown on the screenshot.
Keyboard shortcut: press Ctrl+Alt+4 (Windows) or Option+Command+4 (Mac) to use Album View in iTunes.
iTunes Grid View
The Grid View button has now replaced Album View: grid view allows you to see all your album covers, without any text. Double-clicking on any of the albums will load the songs it contains; you can also filter the number of albums you see at any time, simply by typing some words in the Search box in the top right corner of iTunes' main window. Moving your mouse cursor above an album cover in Grid View will reveal a playhead button: click on it, and the first song of the album will start playing, while leaving you in grid view (vs. loading the content of the selected album). Then, simply use the next track / previous track buttons to play other songs in the album. Notice how the middle, Grid View button is pushed in the screenshot below,
to indicate the current view:
When you are in grid view, click on iTunes' View menu: a Grid View item has been added, and allows you to sort your music by Albums (default), Artists, Genres, or Composers. The Show Header option, disabled by default, will reveal buttons to switch between each sort type; it will also display a slider, which allows you to customize the size of each album cover in the grid view. Finally, the "Group Albums" option separates your music into groups, based on which of the four sorting type you have currently selected:
iTunes Cover Flow
iTunes' Cover Flow view is a split view rendering on top a visual listing of album cover arts (artwork), and a corresponding text listing of the current selection or playlist below. Because of its graphic intensive nature, Cover Flow can take more time than one wishes on large playlists; any left or right scroll has to load and animate the current, previous and next artworks. 
To show your music in Cover Flow, go to View > Cover Flow View in iTunes' main window.
Keyboard shortcut: press Ctrl+Alt+5 (Windows) or Option+Command+5 (Mac) to use Cover Flow View in iTunes.
There is not "best" iTunes View: each has aesthetic and practical advantages for a given situation.
Cannot change iTunes view! (View buttons grayed-out, or disabled)
If the iTunes views buttons are grayed-out (disabled, as shown on the screenshot), and you cannot change the current view, this is probably because you are currently looking at the content of your iPod or iPhone. You will still be able to look at the album covers on your iPhone or iPod itself (unless it is a display-less iPod shuffle), but iTunes currently supports views only for your iTunes library, possibly stored on a network or external drive.