1) Glass Thermometer
This is your basic thermometer and generally you see a kind that can suction cup to the glass of your aquarium, or the other which can be pushed down into your substrate or sit at the bottom of your aquarium moving about freely. The suction cup version I don't really care for because more often than not suction cups don't usually hold onto the aquarium very well and thus fall off and in some cases even break. I would opt for the one that can be pushed down into the substrate because it's not really going to go anywhere, the downfall to some of these is that I find it moves around on its own in gravel substrate due to water movement which can make it difficult to read the temperature, and fish also tend to bump into this thus causing it to move around as well. These thermometers do take some time to reach the correct water temperature but they stay relatively accurate with minimal temperature changes to the water and give you a Celsius and Fahrenheit reading simultaneously.
This style of thermometer is part hydrometer at the top which is more ideal for saltwater aquariums but can be used for freshwater although the salinity reader probably won't be all that beneficial for your tank. The downside is that this can move about freely in your aquarium and make it difficult to read the temperature unless you physically hold the top of the unit. Also, if you have an aquarium lid on your saltwater tank the hydrometer may not give an accurate salinity reading if it hits the lid because that part does need to rest freely on the waters surface in order for you to read it. Or if your aquarium is too small the hydrometer may be too long to work properly as it may rest against the bottom of the aquarium, especially if it's freshwater.
3) Stationary Glass Thermometer
This thermometer is fairly nice because it stays where you place it on the rim of your aquarium. This is comparable to the other 'glass thermometers' mentioned on this post. The downside to this unit is that it may be more prone to wear and tear over time since the numbers and metal on this unit are probably not going to be too algae and water friendly, and it may even tap onto your aquarium glass creating a slight noise annoyance. This thermometer can also be DIY'd a bit to be slightly better, like painting the outer arm to possibly match your aquarium lip better, or adding some type of rubber bumper to the base in order to reduce any possible glass noise. You'll also want to take into consideration how well your aquarium lid/hood will fit with a thermometer like this, and a metal unit like the one shown here can usually be bent a bit to suit your tank a little better.
4) Strip Thermometer
This type of thermometer is pretty common, especially for the unknowing Aquarist, but these are my least favorite of all thermometers. These stick onto your aquarium so pick a spot on your tank you can live with it staying at. Also, not all of these have a Celsius and Fahrenheit reading but that may not bother you. I also find these difficult to read at times because the colors can look very faded and also the readings are not that detailed so you really only end up with a rough temperature reading rather than an accurate one. Also since these are on the outer glass of your tank and not inside the tank it's probably taking into consideration the room temperate and glass temperature more-so than the actual water temperature, thus rendering this thermometer a bit useless for an accurate water temperature.
5) Digital Thermometer
A good digital thermometer is a great thing, this is my second favorite type of thermometer. A good digital thermometer can give you quick precise readings down to the decimal as well as be switched over to a Celsius or Fahrenheit reading. The downside is that you may get a defective or inaccurate digital thermometer and the thermometer is only as good as its battery life in most cases. It generally has a wire that goes into the aquarium which can look a bit awkward in its placement but that's what gives the device its temperature reading (some however may have some type of probe attached to it and adhere inside the tank), and the digital reader is usually suction cupped onto the outside of the aquarium which may fall off at any given time, but probably not too likely to break unless due to electrical issues with the device.
6) Magnetic Thermometer (not pictured)
This is the current thermometer I use in my tanks and I believe it's new to PETCO this year. These are great because you can turn them inside the tank at any angle, it's not permanently adhered to the tank, and it gives a good accurate reading in my opinion although not as easy to distinguish as a digital thermometer. The downside is that this is a bit large in size and I personally wish that this unit was clear rather than white as to be a bit less noticeable. Also if your magnet is too far from the thermometer device the unit will sink rather than float, but you are able to move this around the tanks corners because the magnet is fairly strong.