Use 3-deep blocks for high-wealth
Scroll down below to the stage limits section if you want to know the details, but the gist is that high-wealth houses won't go down to 2x4, instead going to 3x3 at stage 3. Thus the most space-efficient layout for R$$$ uses 6xN blocks (compared to 4xN or 2xN for mid- and low-wealth).
Build out, then up!
Before you begin reading, keep in mind that unlike the previous SimCity games and the newer SimCity, you have to start small. You can't start with tall buildings or compact buildings, and have to sprawl out before you can build upwards. For a beginner it's recommended to build a large city (I'd say 4 or more 2x2 tiles completely full) before upgrading to higher densities and wealth levels. While you can do so with a small town, it becomes quite tricky to manage.
Try forcing the game to place certain lots
One thing you can do to prevent SimCity 4 from building lots that are too large, exp. for R$$ housing, is to align your lots. Simcity 4 will automatically 'merge' lots, however can only do so when their dimensions align such that the combined new lot is a rectangle. You can abuse this.
For example, let's design a zone like this:
R,L,M,H Zone Any,Low, Med, High residential
- Empty space, Trees, Parks
This type of alignment 'forces' your residential zones to create 1x1 or 1x2 buildings which optimizes the space use. The bottom one works very well for medium-density, while the top one is pretty nice for low-density.
You can even do a more advanced trick by mixing medium and high density 1x1 lots (or medium and low density, though that looks less pretty):
This works because all stage 6 and higher buildings are 2x2 or bigger. So you will only get medium-density buildings on these lots (or low density if you build too many of them in a city too small).
Low-wealth medium density lots are only 1x2 or bigger, so you would use this pattern:
Simcity won't merge across density boundaries. Thus it's forced to build 1x1 lots!
However, before you run off and design your whole city like this, it's necessary you learn all about 'demand caps' and 'stage limits', which can prevent simcity building on those 'trick' lots if you build too many of them in a small city. If you for example only built 1x1 lots, you would never get any medium- or high-wealth housing at all because of these stage limits.
If you don't want any high-wealth housing, then make sure you don't have any lots of 3x4 size or bigger. No mansions will ever spawn, because no stage 1 buildings can be built.
Take look at the charts over at this post. These charts apply "Per type" and across your entire region, independent of local topology. This means that before you get your first $$ skyscraper (all skyscrapers are stage 8), not only do you need enough 'demand' for the entire skyscraper (usually several thousand, which means a bar that's completely filled) you also need 43859 $$ residents in your region.
In addition, remember you also still need the regular desirability, land value, and low negative factors in order for the building to grow (and not delapidate).
The charts also have 'percentages' on them. How they work is as follows. First, grab the number of people in your town. Suppose your town has 20,000 R$$ residents. Take a look at the row with the highest population number still below your own. This row indicates 5, 9, 12, 32, 27, 15. This means 5% of your buildings will go up to stage 1, 9% will be stage 1 or stage 2, 12% at stage 1, 2, or 3, etc.
You may have noticed this in-game. As you start out, your R$ people that are moving in only want to go to stage 1 buildings, which are trailers or single houses. After a while of building, you see the stage 2 buildings pop up (the double houses on one tile).
The more efficient houses (in terms of population density) are of a higher stage. The R$$ single-tile houses are stage 3 buildings for example.
So in order to get those 'stage 2' and 'stage 3' buildings for medium-wealth, what you need to do is attract a lot more medium-wealth residents. I'd recommend not upgrading to medium-wealth until you can have around 5,000 or more R$$ residents if you want to make more money. In general, at the start of the game, you'll likely get a balance of 80-20. In other words, until your city is 40,000 souls big, don't bother with medium wealth.
In Rush Hour, Maxis lowered the stage caps, but only for Low-wealth buildings. That's why they 'seem' more efficient. In truth, it really holds only for small cities. Once your city gets bigger, those 4x6 mansions will become quite rare (only 5% of R$$$ wants to live in nothing denser) and rich folks will start to tolerate to live in 2x3 mansions or in apartments, which means more simoleans for you than the equivalent value in R$ housing.
In addition, the really tall buildings (stage 7/8) that can generate a lot of income (and traffic) have much higher tax values in their high-wealth versions. Since having those tall buildings 'requires' getting the smaller buildings through the stage cap system, you can view these as 'worth it' this way too.
Indication of stage
The more densely occupied buildings are generally of a higher stage (buildings are sorted into various stages based on their density level). These charts indicate the size of a typical house for the various wealth levels.
The program at simtropolis has a database with more info. Note that you need XP compatibility mode, it's quite an old program. When stage '123' is indicated that means it depends on 'lot size'. E.g. stage 3 are the same building as stage 1 but on a smaller lot. For even more information you can also check out the pages over at The SC4 devotion wiki on the individual buildings.
Medium- and Low-wealth have two types of buildings, High-wealth only the one.
Stage 1: 4x6, 4x5
Stage 2: 4x4, 3x4
Stage 3: 3x3
Stage 4*: 2x2, 2x3
*Competes with medium-density buildings
High-wealth is exceptional here in that you can see when stage 4 has occurred (and thus how many medium-density buildings you can support) by counting the 2x2 and 2x3 lots. You can potentially upgrade to one apartment for each of them.
Stage 1: 2x3
Stage 2: 2x2
Stage 3: 1x3, 1x2, 1x1
Stage 1: 1x2, 1x3, 2x2 and 2x3 duplexes
Stage 2: 1x1, 1x2 and 1x3 duplexes
Stage 3: 1x1 duplexes
Density of stages
1-3 Low density
4-6 Medium Density
6-8 High density
Higher density zones can grow lower-density buildings if you don't meet the required stage caps. E.g. building high density from the start still only gives you small houses at first.
Stage 6 is a special snowflake, some of its buildings can build on medium density, but others usually cannot. You generally find it on high density, though you rarely see a very tall building in medium density, that's one of those 'lost' stage 6 buildings.
Demand caps are much simpler. They're hard caps on each type of resident (R$$, R$, R$$$, etc.) that apply region-wide. You can raise these quite easily by just building muncipal buildings; parks, fire stations, schools, etc. Most people build enough of these for the cap not to matter. In any case, if demand won't go past zero, this is the likely culprit.