Based on an August 2015 report by OpenSignal, there are more than 1294 brands and 24093 different Android devices. This is a very crowded market with endless variations of new models coming out every year. The display screen has also increased tremendously with the introduction of 7-inch phablets (phone+tablet).
There are endless phone case choices for the top brands (eg. Apple’s iPhones, Huawei ) and models but when it comes to less popular ones, their choices become very limited. This is why universal phone cases are made to fill this gap in the market. Below are a few examples of universal phone cases that will fit 6-inch and smaller display.
Universal Phone Pouch

Pouches are very simple design cases. They do not have back covers, its just a means for protecting your phone. When you need to use your phone, simply remove it from the pouch. Good thing about pouches, they don’t add bulk to your phone, nothing is attached to it. More info here.
Universal Wallet Phone Case

Wallet cases are very popular choice because it has some wallet features in it. You can add cards and money to it so it can come in handy if you want to get rid of your wallet and go very light. More info here.
Universal Clutch Wallet Phone Case

For something much more functional and more compartments, this is a great choice. Ample card slots for all your cards, zip lock your phone inside and also snap fasteners to keep your case closed tightly. Downside is it’s bulkier but since you can get rid of a wallet, this is great for everyday use. More info here.
Universal Phone Purse

Finally, we look at this phone purse. It is really cross between a phone pouch and a purse. Outside is where you slide your phone in/out easily and a snap fastener to keep it from coming loose. Inside is just like a purse with compartments for cards and lots of space for money. Inner zip pocket adds more space for other stuff. Zip lock it and everything stays inside. More info here.