Hanhaba obi is the most casual type of obi (after heko obi) and is usually worn with yukata, particularly if it is one of the 'cheap' ones made of polyester. If a hanhaba obi is nice enough (such as the one shown below, made of silk), it may be worn with a very casual komon. In my opinion, hanhaba obi is the easiest to tie as it does not require any obi makura or obi age, and only rarely needs an obijime, and even some of the more complicated bows are simpler than tying a normal otaiko.
The name 'hanhaba' means 'half width' which indicates its narrowness (anything between 15 and 17cm). It is called so because it is half the width of any other obi.
Nagoya obi is an obi which has two widths - one wide part, where it measures 30cm, and is used for the otaiko (drum) bow that is so commonly seen on kimono, and one narrow strip, measuring 15cm, which is used to wrap around the torso. The narrow length is achieved by folding the obi and stitching it into place, with just enough of the wide strip to form an otaiko bow. Each nagoya obi usually measures between 300cm and 400cm.
Nagoya obi is the one you see most on women. This is because it is the easiest to use to tie otaiko, and is perfect for everyday wear in that sense. Also, most nagoya obi are decorated with patterns suitable for such use (no auspicious motifs, etc).
Fukuro obi is the second most formal obi. It is very commonly used when wearing furisode (long-sleeved kimono). While it cannot be seen in this photo, the fukuro obi is not the most formal as only 60% of one side is decorated. The underside and a part of the obi which will be hidden as it is wrapped around the torso are left plain. This makes the obi less heavy and the lack of intricate work all over allows for lower prices, making fukuro obi a very popular option for formalwear.
Fukuro obi are usually around 30cm in width, and over 400cm long. The extra length is needed in order to tie the intricate bows one sees on furisode.
Maru obi is the most formal type of obi. Its dimensions and formality level are the same as the fukuro obi, yet unlike its alternative, it is embroidered and decorated everywhere on its surface, thus making it heavy and expensive. This type of obi is usually used in weddings, although it can be worn in any other instance a fukuro obi is needed. The only real difference when it is worn would be its weight.
Tsuke obi is also known as 'easy' obi. This is because the obi comes in two parts. One is the narrow strip which is used to tie around the waist, and another is the bow which comes already pre-tied for you! All one needs to do is hook in the bow to the narrow strip and tie the strings around one's torso (and hide them) and voila! Instant obi.
In the case of otaiko obi, the tesaki is sewn to the side and has to be folded in and tied into place with an obijime, as well as having to add an obi makura and obiage.
I am certain there are other types of obi as well, but for now, that's all! Byebye!