My suggestions on these is as always...you're going to get a lot of amateur advice. That's fine, but definitely consult with a professional before you do anything that alters your grading or significantly alters the drainage in your yard. You don't want to wake up and find out you just shifted the drainage into your cellar (if you have one) or first floor. :-)

French drains might help, but do need some rise-to-run (height, basically) to work. Your back yard by the deck looks like it has some. The other two, I can't tell specifically by the photos, but at least the right side yard shot looks like it might be good.

Yet another solution is simply to increase organic matter in the soil (a long-term solution, but workable over a period of years) and increase the penetrability of the soil (faster). That will tend to absorb the water and increase the speed at which water will sink through soil, respectively.

The latter is often done with a 2-4 oz per thousand soap solution, monthly during the season, for a long list of reasons too lengthy to go into here. Hopefully DCHall will chime in with his results as well. Yes, people poo-poo this (generally those who lack chemistry backgrounds and don't understand surfactants and soaps), but it doe work. Combine with organics and it helps keep the soil open all by itself and you can rapidly discontinue the soap.

In my opinion you do not need to spend a lot, but can resolve the problem by re contouring those areas so the drain. When you re-contour make sure that the problem areas have a clear sloping path. Water will always go down hill.

I have a similar problem in the yard in the corner of my patio and house. The problem is caused by a ridge of hard clay the was dug out out of the patio area when it was put in. The clay creates a dam across the drainage swale from that corner. When they did the final grading after it was installed, they did not consider the type of dirt. My solution is to dig a shallow channel across the clay to create a natural looking swale so the area can drain. The new swale is only about 5 inches lower that the surrounding yard and is shaped so the lawn mower does not notice the swale as in moves across it..

Both of the areas in the Picture "Back yard", could be corrected in this way by remove the sod and making the wet spot part of the drainage channel. Dig deeper so when you replace the sod the areas will drain. Similarly in the next three pictures.

In the last picture I am not sure what I am seeing. but it looks like the nature drainage channel goes into a culvert under the road. If so this problem started decades a go when the tree was planted in the original drainage ditch beside the road, It may be only solved by removing the tree, but that would be costly, to cut down the tree, remove the roots, and regrade.. Before I took drastic measures I would dig out the years of accumulated leaves (now soil) so the water has free access to the culvert. I may also use that material to create a dam by filling the are to the right (Picture) of the forked tree forcing the water between the road and the tree. Just adding the dirt to the wet area may be enough. I would have to sit out there studying the area before making a decision on how to proceed. In my estimation this is the only area where you may need to spent money to correct problem.

My "amateur advice" ;-)

"My "amateur advice" ;-)

Yeah, I shoulda phrased that better, sorry. Check any advice you get against a local authority who can measure your pitch and drainage to assure you're not going alter your grade and dump water into the basement or first floor when doing anything drastic. Cleaning leaves is not drastic.

Recontouring could be problematic, depending on how far it goes--and local laws regarding a swale.

In the areas I mention in the picture, the "re contouring " would be to shift a little soil where a ridge is blocking proper drainage. From the picture I doubt if most of the areas would require more redistributing a couple of cubic feet of so soil. All of this could be done with a shovel and a raining day so you had some critique on your work

The road culvert if that is what it is requires a lot of planning and research.

My amateur advice is to get some professional advice. Think about the worst thing that could happen and the consequences. The worst mistake you could make would be to flood your neighbor's house. Second worse would be to flood your own house. I think you need a pro or three to walk the terrain with you and tell you what's what. We can't really tell from your pictures where water might flow nor the effect of adding or removing soil.

Here is a picture from a neighborhood in California where they engineered the water drainage.

From this angle and distance you can see how swales were used to redirect water flowing downhill so that it flowed to the sidewalk or street (through the hole in the curb) instead of flowing/flooding the lower neighbor's yard.