The most versatile vacuum here that will work on virtually any pool surface from concrete to vinyl, that's what makes the Water Tech Pool Blaster Max #1 on this list. It's lightweight at about 5 pounds, and gets even lighter once under water. The rechargeable battery lasts over an hour of run time, which should be enough time to clean virtually any pool. The easy rinse collection bag makes cleaning painless, and it will suck up just about anything that it comes into contact with beneath the water, and that includes algae. Attach it to the end of a pool pole and get to work.
For spot cleaning or just those occasional vacuuming jobs, none do it better than the Aqua Broom Battery Operated Pool Vacuum. It looks like a house broom and will pick up just about anything on the pool bottom, but the bag may be a bit small for whole pool cleaning. In truth, this is the best bang for the buck pool vacuum on the list. It is easy to use, versatile and takes 5 "D" cell batteries. Get 5 rechargeables, and you'll never have to worry about new batteries again. Plus, it is the least expensive handheld vacuum on the list.
If you want a similar item to the Water Tech Pool Blaster Max, but you don't want to pay the price, consider the Catfish PPV Pool Cleaner. It has an easy to clean bagging system, it's lightweight for ease of use and it will run for a solid hour on its rechargeable battery. While a great cleaner, it's sometimes difficult to turn on and off switch. Wet hands slip while turning it and some people have a hard time using it properly. That doesn't mean it isn't a good pool vacuum, but in that one respect, ease of use is suspect. However, it is one of the least expensive vacuums here, so it is still a good deal regardless.
If you have major leaf problems in your above-ground or in-ground pool, the Leaf Gulper Pool Vacuum is the way to go. Although it is made primarily to pick up sunken leaves, it will do a credible job picking up other debris as well. The large bag will capture a pools worth of leaves, just attach this unit to your garden hose and a pool pole, and have at it. The pressure from your hose creates a high pressure jetting system that funnels leaves into the bag. Suggested use is only for concrete or vinyl, but it is an inexpensive and effective way to remove the leaves from the bottom of your pool.
This is the most unique pool vaccum on the list. The GAME 4855 Spa and Pool Vacuum is easy to use, requires no batteries, hose or pole attachment, yet it will do a good job of vacuuming any pool or spa bottom. It is powered by you, working the pump handle up and down to achieve adequate suction at the tip. It includes a leaf skimmer, slide-on brush and both a dual nozzle and a wide nozzle. You will have to get into the water to use it effectively, and it may not be the best choice for a large pool, but for spas, inflatables or spot cleaning, this one will do the job.