If you just have 1 lower level in each higher level unit you will not be able to separate out the within from the between variation - they will be confounded and the two variances will not be identifiable.

The answer to your question depends on your target of inference; If primarily you want to say something about  the between-difference then you want lots of higher -level units and the lower level units can be quite low - classic example is households and twins - you cannot force people to live in big households and twins never get above 2 - so you will be able to say little about specific households and twin pairs with any certainty but you will be able infer about between-differences if you have lots of the higher level units. The same often goes for panel data where the higher level  is an individual and they are measured on relatively few occasions. You can often infer between -person variation but not say much with confidence about a particular individual.

 The other target is when you want to say something about the particular higher level units as well as infer about the variance between higher-level units, The classic example is pupils and schools - you need lots of schools (say a 100) and lots of pupil in schools ( eg a minimum of 25 pupils). Of course modern estimation can cope with imbalanced data with a different number of pupils  in a school and the school random effects based on few pupils will be shrunk back to the overall mean- that is the inbuilt  precision-weighted estimation of random effects

on the latter see

https://www.researchgate.net/publication/225303298_Contextual_Models_of_Urban_House_Prices_A_Comparison_of_Fixed-and_Random-Coefficient_Models_Developed_by_Expansion

and

https://www.researchgate.net/publication/252146040_Do_multilevel_models_ever_give_different_results

and on designing a multilevel study see,

http://www.bristol.ac.uk/cmm/software/mlpowsim/

Article Contextual Models of Urban House Prices: A Comparison of Fix...

Article Do multilevel models ever give different results?.

I agree with Kelvyn, but have some reservations on his dealing with twins and households. In the first edition of Snijders and Bosker it is said that the samples at both levels should be random (exchangeable). Twins are only two in their own population so for each pair of twins your have the population, and not a sample. There seems no need to estimate any population parameter (as long as a calculation can be made). The average 'population' height of the twins can be calculated. In schools classes do not have infinite populations, but small finite ones. Would there be no need to include finite population corrections? 

Interesting........... I see twins as a stochastic outcome and very unlike the fixed classification of Males and Females that may be seen to exhaust the possibilities of realizations of gender .

Indeed the second edition of the Snijders and Bosker book gives the following examples of macro and  micro amenable to multilevel modeling

families                 children

litters                    animals

Morover, the are some excellent  papers in this area

S. Rabe-Hesketh, A. Skrondal, and H. K. Gjessing ( 2008) Biometrical Modeling of Twin and Family Data; Using Standard Mixed Model Software , Biometrics 64, 280–288, DOI: 10.1111/j.1541-0420.2007.00803.x

and for households

HARVEY GOLDSTEIN, JON RASBASH, WILLIAM BROWNE GEOFFREYWOODHOUSE and MICHEL POULAIN ( 2000) European Journal of Population 16: 373–387, 2000.

and families

Rasbash, JR, Leckie, GB, Jenkins, J & Pillinger, RJ 2010, 'Children's educational progress: Partitioning family, school and area effects' Journal of the Royal Statistical Society: Series A (Statistics in Society), vol 173, no. 3, pp. 657 - 682., 10.1111/j.1467-985X.2010.00642.x

It is interesting, because when we are dealing with small samples within schools the estimates are shrunken towards the mean, but would it not be over-shrinking if we deal with a large part of the population within a level?

That was my point about the target of inference - no one would wish to infer to each and every specific twin sibling pair - it is likely to be of little interest per se and it would be very uncertain as based on two observations. But a genuine target of inference is  the within- and between- variances across all pairs of twin and these will be based on all pairs that you have and this could be reliably estimated. 

This paper powerfully sets out the importance of the multilevel model in such circumstances

Guang Guo and Jianmin Wang (2002) The Mixed or Multilevel Model for Behavior Genetic Analysis, Behavior Genetics, Vol. 32, No. 1,  37

Furthermore and in relation  to shrinkage,  the variance at level 2 summarizes the differences between level 2 entities; but this not the variance of the shrunken residuals. but variance of the raw mean residuals.. The level 2 variance is not the estimated between group variance of the  sample, but the estimated between-group variance in the  population.

Typically (with max likelihood) estimation we estimate the between and within variance and having estimated these values we MAY  go onto estimate the shrunken residuals at level 2 - but we may choose not to do this ; indeed the SPSS implementation does not have this facility as it mainly geared up for longitudinal analysis  and the level 2 entity - when it is the individual - is usually of little interest per se. And this brings us back to my original answer in terms of the target of inference.