Meaning lots that I made (with one or two exceptions) and that I always place when I am starting a new 'hood.

Community lots:
- Ingres Academy: painting and various musical instruments
- Tesla Library: library, chess and computers
These two make sense only if you have the "Sims study on community lots" mod. They look identical from outside so I place them next to each other or, even better, across the street from each other. Other Sims love to visit them but they mostly just stand around and only play chess.
- the gym
- the pool
Only if such lots are not already on the map.
- "Marry-in-a-Hurry" wedding chapel
- the Disco. With a DJ and a bar. It also has a karaoke machine but that's optional: I tend to grow tired of all that terrible singing.
Private lots:
- a church with a vicarage
Again, if not already on the map. Small (less than 20.000) in a starting 'hood and large later on; the vicar has to earn this one. He or she is always in "the priest" career (mod), of course.
- the police station
- the high school
- the dean's office, if I play University. I usually do.
All are completely furnished so I have to cheat if I want to put in a policeman or a principal/dean. They look well on the map but I only use them for stories. And I am afraid my Sims don't want to be bothered by elementary schools.
Exceptions:
- "3-in-1" bookshop. With some small modifications. The first place that my Sims visit in any game.
- a clothing store: only if needed. I made some of my own but I mostly use Maxis' ones.

There are others (a museum, a sauna, etc.), but the list is long enough as it is and they are not obligatory.

Do you use similar lots as well?

I'm not sure what you're asking or if I'm not the right person to answer.
Do you mean which lots we use when we create a brand new neighborhood or which lots we have recurring in our sub hoods? (If you mean the former I can't answer, if you mean the latter I'm guessing it includes a clothing store, a grocery store, some kind of park and apartments/houses. I can look it up more closely if you want )

That's too many to place every time! Different communities need different number and variety of community lots.

There has to be a place to buy groceries - unless the premise of the neighborhood is that all food except the original amount in the refrigerator has to be produced in-game. There has to be a place to buy clothes - unless the premise of the neighborhood limits sartorial choices. There has to be a restaurant to get past the "eat out" want on dates - unless the premise of the neighborhood - you get the picture. A big city needs lots of different community lots. A small town, not so many. Starting Widespot has one store for both clothes and food, a swimming pool, and a make out spot which is nothing more than a bench and some bushes. Different people add different lots in different orders; or they keep it residential and add a downtown.

I have a small handful of lots in the bin that I made and have put down in multiple neighborhoods - the restaurants I've uploaded here, a library for Widespot, and so on - but I don't like to go to the same lots over and over. I get bored of them, and I like each neighborhood to have a distinctive culture. Turpitudia and Widespot and an agricultural colony on a new planet should have distinctive architectural styles and different ways to work and play. If they don't, what's the point of making a new neighborhood at all?

Communities change. I add new buildings and tear down or repurpose old buildings as the needs of the neighborhood change.

Peni is right-you don't need a lot of community lots-just a few to keep things functioning well-'

A grocery store
A movie theater, roller skating rink, or similar
A clothing store
A playground or a park with options for fishing or swimming
A 'teen hangout'

Overloading the neighborhood with too many places to go tends to make too many choices. The pixels have simple needs. They don't need much but make them happy with things they do have.

Tinsel Town is too overloaded with places and I"m about to shrink them down in size. There is such a thing as too many choices.

There is NO such thing as too many community lots

I like to use the group phone function and send sims on group outings. They can go anywhere, eg. Knowledge sims enjoy a trip to the library, active sims like a trip to the gym, nature lovers love to visit the fishing pond and art lovers enjoy going to the art gallery (just a number of examples, there are more)!
There is always a good reason for a sim to invite friends to a restaurant as well, and some of my sims perform for tips, which is their only income, so it is hardly worth it to sit around at home for them.
Kids and babies - just phone the nanny
O course, soms sims also has to run their owned businesses: the Grocery, the Garden Shed, the Fashion Boutique, the Pottery Shop, the Florist, the Light Shop and a few more, and I like to send my sims to buy from their local shopkeepers too.
And sometimes, they go to Downtown too.

They didn't actually ask which lots they should use; just which ones other people used. What lots are necessary are the ones you want and use.

I generally don't use community lots, but have residential lots stand in for community lots (I find them easier to work with for posed photos).

Back when I did use them for gameplay, my game spent ages loading lots, which didn't exactly make community lots any fun. I preferred keeping all or most buying needs at one lot, and whatever other needs the sims had in a community lot on as few lots as possible. To reduce travel time, I preferred having one or two somewhat decent sized lots with many opportunities for buying needs and fun, rather than several lots with just one or two options.

My sims have now discovered internet shopping (buying stuff via mods), and I have various reasons to prefer residential lots for most things (I teleport them in), so they're covered XD

My new story hood has a couple schools (combined elementary/middle + a high school), a hospital (alright, two hospitals, but for important reasons), a street or two with some shops, a graveyard, maybe a church (if I end up needing it again), possibly a movie theatre, likely a grocery store (used it in my previous setup), a skate park (if I need it again), and likely some more as needed.

So real. My old computer took foooooreeeveeeeeer to load a lot, so I would avoid community lots as much as possible. I pretty much only went to owned businesses because I had to for the BACC challenge, and I would maxmotives some 2 or 3 times while there just so I could cut down on the number of trips back and forth. Now that I have good computers and loading screens are very quick I have no problem with community lots, they're integral to my gameplay.

I play integrated BACC style. Nearly every lot is owned and it's built from the ground up with money my sims can make. The first lot was the residential farm with fishing pond (or sometimes I make a dedicated pair of fishermen) this is to feed the community. Most times the farm is also a home business. So shelves with fresh produce.
Sometimes though i have had them run a small general goods store.

Next on my list is the pub because all small towns have one. This will be booze, poker, pool, meals. This gives the adults something to do and a place to go.

A service station. (a gas station if you are American) The servo as we call it sells odds and ends.This time it has grocery freezers, a small game rack, a magazine rack, an electronics kiosk for your mobile phone etc, snack machines and now over at the petrol pump two cars for sale. I know you wouldn't normally buy vehicles but its level 10 and doing so well and the community desperately needs cash and flogging cars to townies is a good way to make some.

A beach lot. This is free. The main founders (the farm) bought a bathroom and picnic area for it. One of the other families bought it a hammock. (he was desperate for whohoo places) I really like hoods where I can place a beach lot as it offers a lot of things to do plus they can comb for shells and flog those off to townies too.

A meeting hall/wedding venue/dance hall type of place. I just finished building this. Meaning my sim who runs this can now go into politics and this area can have someone to bat for them in sim city. It's like a big barn with a stored wedding arch, lots of chairs, bingo, a stage with instruments (I must buy them a microphone) And a small play ground outside for the kids.

There is also a gym
A coffee shop
And brand new clothing store. So new he hasn't even had opening day but just bought it.

the primary school is one side of a residential lot and they really need a clinic. They also really need a police station and a fire station. But money for such buildings must come from the earnings my sims can make off townies. I would also like a church, all small towns have a church but I imagine the 'dance hall' serves as such for now.

This hood is extra slow as I started it with one sim. So all the families living there are one of his six kids and or grand kids. It takes a lot of cash to build all of these buildings as well as having suitable sims to run them and every cent comes from townies buying goods and services.I decided there would be no money perks or genie lamps this time.
But yes I will eventually have all of those lots and more.

there is satisfaction in knowing that X lot was earned through hard work, or going to the beach and knowing that the barbecue and table/chairs was donated by the founder. If he were richer I would have him donate money for an entire lot but he gave each child at least 8K on moving out (since no 20 k handout mod)

I know this particular pain-in the past I used to avoid community lots like the plague, but with every successive improved computer, I started using them more.

And now with this new rig (SSD, 1 T drive space, whopping 8 gig memory from graphics card) it only takes 2 minutes tops to load the game from start to inside the neighborhood and then 20 seconds to move from a home lot to a community lot

Already I've been sending the pixels on a lot more trips to community lots for fun and other purposes. They're not homebodies any more!

I feel bad for not sending my sims out more now. XD I get lazy.

My list then.

Some of my lots are very old, I have built them in former hoods and can just grab them from the lot bin when I need them; some are also downloaded ones that I had for a long time.

I don't play an integrated hood the way Jo does, but my hood does function like a community, with sims supporting, needing and interacting all the time. My sims buy from each other and also teach each other anything from skills to Tai Chi, share hobby tips, etc. And I have a couple of freelance performers who has no other income.

Fishing pond: always comes first, and it will be the first place all the sims will visit.
Bar/Pub - at least 4 small ones, so that they can go bar crawling, offering different activities (one has karaoke, one has 2 pool tables, one has poker and one has a small band stage).
Library
Gym
Quick stop shop
Restaurant (or 3)
Parks - I have a number of them offering different things, eg, an art park with easels, a rock and roll park with a stage, a sport park, etc.
A community hall with all kinds of activities, including the welfare.
A number of owned businesses, as mentioned above.
A music performance venue
A learning center.
A public swimming pool.
A bowling alley
A roller-skating rink.
A sport venue