goomwwm is a mouse-centric stacking window manager. That means that new windows are opened above others, you can move them around and the focused window will stack above any windows it overlaps and you can resize them to arbitrary sizes, uses a alt-tab (mod-tab and mod-grave really) window switcher to toggle between open windows (tab between all windows, grave between windows of the current tag only) and lets you minimize windows - just like you'd expect from a traditional stacking window manager. You can move/resize with the mouse, but there are keyboard controls to move and resize windows. It is these keyboard controls that make it feel like a manual-tiling window manager because it is very easy to position windows in a tiled manner and there are some conrols that really help with this:

mod-d will resize the focused window to be the exact same size as the window directly below it
mod-f makes a window fullscreen
mod-v resizes all windows stacked underneath the focused window so that they are tiled vertically (occupying the same space as they did before)
mod-h is the same for horizontal tiling
movement is aligned to a 3x3 grid
the grow and shrink resize the window by an amount that makes tiling on the grid easier (there is also a more fine-grained grow/shrink that doesn't align to the grid)
mod-shift-movement will swap the focused window and the closest window in the direction of movement - this swaps both windows sizes and their positions
mod-home sets the window height to the height of the screen
mod-end sets the window width to the width of the screen
mod-shift-movement2 "snaps" the focused window to the edge of the closest window in the direction of movement2
mod-return will grow the window to fill all available space without overlapping other windows
mod-backspace will shrink a window to fill all available space without overlappinp other windows

By default, mod is mod4 (the windows key), but can be set to anything you like.

movement being the keys to move windows, by defualt the cursor keys.

movement2 being the keys to select/focus windows, by defualt i, j, k and l.

On top of this, you can set rules which basically allow you to run certain commands on specified windows/applications automaticlaly and rulesets which are sets of rules which you can trigger through a keyboard command. A ruleset you can find on the goomwwm website is to automatically tile windows like you would in a dynamic tiling window manager like awesomewm (eg a main area and a side area), you can then use the "swap" commands to swap the windows in the main area with the other windows as needed.

This makes goomwwm feel very much like a manual tiling window manager, yet it still has solid support for stacking and, in fact, always stacks windows by defualt. This makes it more flexible than it would otherwise be without giving up any tiling or keyboard-centric goodness.

Of course, being a border-less, title-bar-less super minimal window manager makes it also look like a tiling window manager, which are traditionally just as minimal.

I'm sure I didn't explain that very well, so I'd suggest giving it a try in Xephyr or Xnest or something. Its easy to get running (git clone ...; make; ./goomwwm -- takes about 2 seconds to compile on my laptop) and only depends on the usual xlib related libs and dmenu. Or, if you don't feel like trying it out, you should at least glance at the tutorial: http://aerosuidae.net/goomwwm/tutorial