Attendre quelqu'un vs s'attendre à quelque chose = to wait vs to expect in French

It is interesting to notice the difference of meaning and usage between the active verb attendre (to wait for / to expect) and the reflexive verb s'attendre à (to expect).

To understand their respective usage, it's important to consider the nuances of the English verb to expect: It can mean either simply to wait for [something/someone], but it can also carry a sense of longing, personal expectation towards what's going to happen.

When to use "Attendre quelqu'un" and "s'attendre à quelque chose" in French

Look at these two sentences:

 -> Here they're simply stating they're waiting for his arrival, if anything they're actually happy he's coming.

 -> Here on the other hand, there's expectation for what his arrival might do, here it's actually apprehension, a slight sense of discomfort or fear at the idea of his arrival.

attendre [quelqu'un] ou [quelque chose]  
=  to expect / to wait for [someone] or [something] 

Note that (in this context: to expect/wait for [someone/something]) the verb attendre is NOT followed by a preposition in French, and is used with direct object pronouns (le, la, les, nous, vous, me, te).

Attendre can also mean to expect [someone]/[something] in a neutral or positive sense.

ATTENTION: when talking about pregnancy, you use attendre:

attendre [quelque chose] de [quelqu'un]   
=  to expect [something] of [someone] 

Note that the preposition de would be followed by stress pronouns (moi, toi ...) to express of me, you....

s'attendre à [quelque chose]  
=  to expect [something] (to happen) 

To say to expect something in the sense of putting expectations on what follows, you will use the reflexive verb s'attendre à + [something].

ATTENTION:
You cannot use s'attendre + a person to say to expect someone.
You will instead use the simple attendre or a longer sentence (e.g., to expect to see someone):

To avoid repetition, you can use the adverbial pronoun y (à + noun).

attendre que + Subjonctif clause
= to wait for [something to happen] / [someone] to do [something]

This structure is used when you wait for [someone/something else] to do something. Here the waiting is neutral, carrying no connotation of dread or expectation. 

You use the simple form attendre + que + person doing + verb in Le Subjonctif 

s'attendre à ce que + Subjonctif clause 
=  to expect [something to happen] / [someone] doing [something] 

This more complex structure is used when you expect someone/something else to do something. 
Here the waiting is coloured by personal expectations, usually (but not always) negative ones.

You use the reflexive form s'attendre + à ce que + [person doing] + verb in Le Subjonctif

See also Conjugate regular verbs in the subjunctive present in French (Le Subjonctif Présent)