My answer every time, in every situation, is an Absolutely Yes, you should. Even if you do not think you need one after finishing your open water certification, there are a ton of reasons why it could benefit you, and nearly no reasons why not to keep one. Let's start with the reasons why people say they do not keep one.
I don't want to buy one.
Okay, lets kill this reason real quick. SCUBA is an expensive hobby, nobody is pretending it is not. Compared to the cost of every other aspect of diving, what is an extra $5-$10 for a nice dive log? I have found multiple small, water resistant logs for about $6. They hold anywhere from 30-50 dives, so unless you are diving every week, it will last you a while. I am personally a fan of the non water-resistant logs (the ink doesn't smear everywhere when I look at it funny), and my favorite log holds 101 dives (with a separate page for each dive), and was less than $7 online. If you are really concerned with the cost, there are ways to log dives for FREE as well. There are plenty of online/downloadable programs/apps for your computer/phone that allow you to log your dives. If you want to go as basic as possible, a handmade spreadsheet can work as a dive log as well.
2. It takes too much work to keep a log
Alright, I admit there are small amounts of effort needed to keep an up-to-date dive log. I personally enjoy sitting and logging my dives afterwards, but you can make it a fun activity if you aren't the type who likes sitting and documenting things. We like to log our dives during post-dive drinks. After a day of diving, we pick our favorite restaurant, order some adult beverages and apps, and log our dives together. We talk about how the dives were, what we saw, funny things that happened, and sign each others' log books. It is a great way to look back and "debrief" the dives as well as a fun activity for the family/dive buddies. We personally put quite of information into our logs, but a basic log will only take a couple minutes to fill out, especially if you keep up with the log after each dive day. Still too much effort? Okay, get a computer that keeps the log for you. A good number of dive computers now include a program so you can connect to your phone or computer by cable or Bluetooth and download your dives. All of the important information auto-populates the log with no extra effort on your part.
Now that we have talked about the reasons NOT to log, lets talk about the good stuff. Why keep a dive log after initial certification?
1. Keep track of different equipment configurations and weight
This applies to divers that have multiple sets of equipment as well as those who use one set for everything. For every different mix of equipment you use, the weight you need to add will vary. The thicker the wetsuit you use, the more weight you need. If you use a backplate/wing some dives, and a jacket-style BCD other days, the weight will be quite different. If some days you dive with gloves/hood and other days just the wetsuit, those small amounts of neoprene will change your weight by a couple pounds. If you have a variety of wetsuits and equipment that you switch between, this very quickly becomes impossible to remember. Add in the difference between salt and fresh water weight required, and you really could benefit from a dive log.
2. Keep track of experience
While this may not seem important to you after initial certification, it could end up being the line between being able to go on a specific dive or not. Some charters require proof of similar experience or an advanced certification for more difficult dives. For example, if you want to dive for megalodon teeth in the Cooper River, the charters will frequently require either AOW or proof of similar/a higher quantity of dives. Often, dive charters will want to see this information prior to dives that are deep, blackwater, or high current. They may not allow you to participate, or may take you to an alternate dive site, if you do not possess this documentation.
3. Continue your dive education
You may have decided that all you plan on doing is an Open Water certification and then do vacation dives that are shallow, in warm water, and guided forever. Okay, there is nothing wrong with that. However, a lot of divers find that as they get more comfortable with diving, they want to explore a larger variety of things that they had no interest in to begin with. This leads to them wanting additional certifications that they didn't plan on in the beginning, in particular Self-Reliant or Technical Diving. PADI Self-Reliant diver requires 100 logged dives prior to starting the course, and Technical Diving courses require at least 30 logged dives with at least 10 logged Enriched Air dives over 60ft at least 10 logged dives over 100ft (or a Deep Diver course completion). If you decide you want to try either of these kinds of diving and have not logged any dives beyond Open Water, you could be waiting months or even years to log enough dives to start.
4. Plan dives
If you log plenty of information in your dive log, you will be setting yourself up for success in future dive planning. Using information from previously logged dives, you can see how your air consumption differs for different depths, conditions, and gear configurations. This allows you to appropriately sit down with your buddy and plan out your next dive. The more information/dives you have logged, the more accurately you can make the plan for air consumption. This also allows your buddy to see your experience level in that particular type/environment of diving. Wouldn't you be more comfortable diving with a buddy that has proof of similar experience instead of one that just says they are good?
5. Keep track of dive sites
If you tend to frequent different sites, but like coming back to ones you previously enjoyed, a dive log can help you. I will use the Bonaire example. Bonaire has 80+ dive sites, and often once you have been there, you would love to eventually return. If you dive 7 days, 3-4 dives a day, you end up with 21-28 different dive sites that you may need to remember years in the future when you return. If you LOVED one site, would you want to forget which one it is when you come back? Or would you like to waste a dive on a site that you tried the first time and hated? What about that dive site that you found a very easy way to enter, or maybe you have notes about an area you want to check out the next time? All of this can be accomplished with a log. With a dive log, next time you visit, you can look at what sites you have already been to, which are worth revisiting, which ones are ones to avoid, and different bits of information you have about each one.
6. Write down memories
Did you see an octopus that day? What about a super rare fish? Was this the day that you found that 6 inch megalodon tooth? Or maybe just that 2 inch one you love anyway? By writing down the experiences of the dive, it gives you something to look back on during those dry months you can't be in the water. Most people like to write a note or two about the things they saw, some people go as far as adding pictures to the log, or making a scrapbook style dive log. In addition to fun memories, the comment area can also be for thoughts of the particular charter or shop that you used. If you loved it, write that down! If you hated it, write that down too. It helps to be able to look back at your personal opinions of the company when you are planning future dives and deciding who to go with.
7. Have fun logging
It can be a fun activity to wrap up a great dive day. Grab your buddy, get some food, talk about the awesome dives you did. It is a great time to discuss what went right, what went wrong, what to do differently next time, and all those cool things you saw. It is also a great time to break out the photos you took and share them or to count/photo those awesome shark's teeth (or pile of golf balls) you found while diving.
Now that we have discussed why to log, let's talk about different types of dive logs. Different types of logs have different benefits. A type of log that is a good fit for one diver may not be the best for another, and some divers may prefer to log their dives using more than one method for redundancy.
Handwritten log - A traditional dive log can either be waterproof or not. It contains places to write all of the information about each log. They frequently have spots for dive center stamps and buddy signatures. It normally includes space in the log for emergency contact and insurance information. It can also include a page for gear purchases/service dates and checklists for travel. Some dive logs are in a binder style, and pages can be added on later instead of starting a new log. Care must be taken not to lose these logs on a trip, forget them at home, or get them wet if non-waterproof.
Dive computer - Your dive computer most likely has a log in it, however you need to use caution if only using this. Some dive computers can only hold ~20 logs at a time and even the larger ones can only hold 100-500 logs. This leads to old log information being deleted. You also don't have the opportunity to have buddy signatures or notes. You cannot see where the dive location was, only what dive number and your dive profile. If your computer suddenly dies, you have potentially lost your log forever.
Computer program - Frequently, dive computers come with a computer or phone program to upload logs to. These logs are similar to the computer logs with the ability to hold more logs and add notes. Unless they connect to the internet, these logs can be lost if the computer dies and there is no backup. If your computer does not come with a logging program, there are multiple ones online available for download that do not require internet connection to use after download.
Internet Log - There are many websites that have a web browser based dive log. These can be similar to the computer program logs above, but are not saved on your computer, instead saved on the website. This has positives and negatives. On one hand, you can access the logs from anywhere that has an internet connection, whether it be your phone, a tablet, or computer at home. On the other hand, they require an internet connection to view the logs, making logging in more remote areas impossible. If the website is ever taken down, or has a major problem, you run the risk of having all of your logs deleted.
What to record in a log
What divers record in their personal log can vary, but there are a few things that should be included every time. You should always have your max depth, bottom time, and air consumption. Time in/out and start/end pressure, as well as the date, location, and salt/fresh water are also great pieces of information to include. For the best use of a dive log, you should also include gear configuration, exposure protection, weight, and conditions, like temperature, current, and visibility. Buddy verification can be important if you intend to use the dives to take a class later, and a comment section can be a good catch-all for any other information, memories, and thoughts on the dive. If this dive is part of a course, you should also include the course, dive number for that course, and the instructors name. That can be valuable if somehow the course is not recorded correctly and you need to prove you did all the dives for a certification or specialty, especially when the course was taken at a location/shop that you do not normally use, or is far away from home. The more information you include, the more helpful the log can be for future dive planning, or just to look back at some fun memories.