Yes, but as with anything in life, there are things that you can do to make them more effective. Just simply "doing puzzles" does not guarantee success.
Do tactics trainer and tactical problems help you?
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@Irmall01 What do you think it is you can do to make them more effective?
Note my rating - I am by no means a strong player so take my comments with a grain of salt. What I am going to say is based heavily upon Dan Heisman's novice nooks and the 400 points in 400 days articles that Michael De La Maza wrote as well as my own experiences. Feel free to google those if you want to go and read what they have to say for yourself.
Basically what it comes down to is making the tactics you study "stick" in yoru mind. You really need to internalize what is going on so the next time you see the problem or a similar motif you recongnize it without much effort.
One way to help make them stay in your long term memory is repetition. Based upon my experience it is better to spend 5 hours studying 100 puzzles 5 times then spend 5 hours studying 500 different puzzles with no repitition. You should repeat a set of puzzles until you get most of them correct just by recognition. Once you master a set then start a new set and review the old set every so often to make sure you don't forget them.
If you don't repeat puzzles like this and add new ones as you improve, I think you must spend a lot of time analyzing your missed puzzles to fully understand the ideas behind the tactic. I think you can still improve this way and which way works best probably depends upon the person.
Just in case it isn't obvious, I think a sure fire way to waste your time is by doing puzzles with light review of the incorrect answers. I did this for years - buy a book, review the problems, buy a new book, review the problems - but never got significantly better. I have gone back and converted many of those positions into elecronic format and used software to track my progress and it is shocking how many of them I could not solve. Obviously my first round of study didn't provide much benefit.
Many websites (probably this one, I'm not sure since I'm not a paid member) will automatically present your missed puzzles back to you more frequently so you may not have to think about it. However, I urge you to find out before you invest significant time.
Good luck! Hope this has been helpful.
I usually play with "Tactics Trainer" about 1/2 hour a day and for the most part get very frustrated. My rating in this particular task is about 1700, but you can easily drop it back to 1400 +- if not careful.
However, your suggestion to repeat puzzles on an ongoing basis sounds very interesting, but how to do we that in chess.com?
This last question is for anyone who may know the answer... 
yes they do
They do help. How exactly to best use them is a topic that has differing opinions, but like anything, you get out what you put in.
I forgot to mention earlier, the best puzzles come from your own games. Find the tactics you missed and start your own database of problems. Over time this plugs the gaps in your knowledge and every problem is relevant since you missed it in your own game.
For diamond members who have access to the Chess Mentor there are all kinds of great tactics courses. Whenever I get frustrated with the TT I just go back and hit some of those again. Seems to help to think of the TT as a tactics tester and the Chess Mentor courses as the true tactics trainer. Of course at my age it's not uncommon to 100% a course then come back a month later and find not all of it "stuck". It's possible that I may have done some of the CM courses quite a few times.
I was wondering if the chessmentor tactics problems, chess tactics trainer, and general tactical problems actually help you get better at chess. Will doing them actually improve my rating or is it there more or less to gage how much ability I already have rather than to improve it? Has anyone done them and noticed an increase in rating due to the excercises? Thanks a lot