Interface builder (iOS 9+)

Just drag a UIView to the table. In storyboard, it will sit at the top below your custom cells. You may prefer to name it "footer".

Here it is shown in green for clarity, you'd probably want clear color.

Note that by adjusting the height, you can affect how the "bottom bounce" of the table is handled, as you prefer. (Height zero is usually fine).

To do it programmatically:

Swift

override func viewDidLoad() {
    super.viewDidLoad()
    self.tableView.tableFooterView = UIView()
}

Objective-C

iOS 6.1+

- (void)viewDidLoad 
{
    [super viewDidLoad];

    // This will remove extra separators from tableview
    self.tableView.tableFooterView = [UIView new];
}

or if you prefer,

    self.tableView.tableFooterView = [[UIView alloc] initWithFrame:CGRectZero];

Historically in iOS:

Add to the table view controller...

- (CGFloat)tableView:(UITableView *)tableView heightForFooterInSection:(NSInteger)section {
     // This will create a "invisible" footer
     return CGFLOAT_MIN;
 }

and if necessary...

- (UIView *)tableView:(UITableView *)tableView viewForFooterInSection:(NSInteger)section
{        
    return [UIView new];

    // If you are not using ARC:
    // return [[UIView new] autorelease];
}

iOS 15:

This year Apple introduced a new modifier .listRowSeparator that can be used to style the separators. you can pass .hidden to hide it:

List {
    ForEach(items, id:\.self) { 
        Text("Row \($0)")
            .listRowSeparator(.hidden)
    }
}

iOS 14:

you may consider using a LazyVStack inside a ScrollView instead (because iOS is NOT supporting appearance for SwiftUI lists anymore).

iOS 13:

⚠️ This method is deprecated and it's not working from iOS 14

There is a UITableView behind SwiftUI's List for iOS 13. So to remove

Extra separators (below the list):

you need a tableFooterView and to remove

All separators (including the actual ones):

you need separatorStyle to be .none

Example of usage

init() {
    if #available(iOS 14.0, *) { 
        // iOS 14 doesn't have extra separators below the list by default.
    } else {
        // To remove only extra separators below the list:
        UITableView.appearance().tableFooterView = UIView()
    }

    // To remove all separators including the actual ones:
    UITableView.appearance().separatorStyle = .none
}

var body: some View {
    List {
        Text("Item 1")
        Text("Item 2")
        Text("Item 3")
    }
}

Note that a static list doesn't show extra separators below the list by default