Why didn't Harry receive presents or fan mail?

There are definately methods to stop Harry from recieving all that fan mail which are detailed in the Pottermore escrita Owls by J.K. Rowling.

Should a witch or wizard not wish to be sent letters (or tracked in any other way), he or she will have to resort to Repelling, Disguising or Masking Spells, of which there are a great range. It is possible to protect yourself from all correspondence, or all but that carried by a specific owl. If a witch or wizard is determined not to be contactable by a persistent creditor or ex-boy or girlfriend, they might try a masking spell specific to that person, but this ploy is easily circumnavigated by asking somebody else to send the owl. In general, it takes strong protective magic, and a willingness to forego a lot of birthday cards, to avoid the attentions of Owl Post.

Trained owls are expensive, and it is quite usual for a wizarding family to share a single owl, or else only use Postal owls.

The rest I am afraid is speculation, but I see a few plausible theories:

1. Dumbledore could have cast some of the spells we see above without Harry's knowledge. This would allow only letters and packages from correpondents that Dumbledore deemed fit.
2. Dumbledore may have asked the Owl Postal Service to not forward letters to Harry.
3. The owls only deliver post at breakfast, so overnight Dumbledore may have had someone like Filch sort through the mail.
4. Many people did not know where Harry was living. So after 10 years of their packages being brought back the community as a whole stopped sending the packages.

Just a personal note, I doubt Dumbledore would have roubado any of the mail. If he was intercepting it, I am sure he would have marked it "Return to Sender".

Your suggestion is not impossible and difficult to rule out, but I can offer a couple of data points.

Durante os eventos de Harry Potter ea Ordem da Fênix harry receives lots and lots of mail in response to his Quibbler interview while Dumbledore was still headmaster.

She gave the delivery owl a Knut and unfolded the newspaper eagerly while Harry helped himself to orange juice; as he had only received one note during the entire year, he was sure, when the first owl landed with a thud in front of him, that it had made a mistake.

'Who're you after?' he asked it, languidly removing his orange juice from underneath its beak and leaning forwards to see the recipient's name and address:

Harry Potter
Great Hall
Hogwarts School

Frowning, he made to take the letter from the owl, but before he could do so, three, four, five more owls had fluttered down beside it and were jockeying for position, treading in the butter and knocking over the salt as each one attempted to give him their letter first.

'What's going on?' Ron asked in amazement, as the whole of Gryffindor table leaned forwards to watch and another seven owls landed amongst the first ones, screeching, hooting and flapping their wings.

Harry Potter and the Order of the Phoenix - pp.509-10 - Bloomsbury - Chapter 26, Seen and Unforeseen

Not all of this mail is nice.

'This one's from a bloke who thinks you're off your rocker,' said Ron, glancing down his letter. 'Ah well ...'

'This woman recommends you try a good course of Shock Spells at St Mungo's,' said Hermione, looking disappointed and crumpling up a second.

Harry Potter and the Order of the Phoenix - p.511 - Bloomsbury - Chapter 26, Seen and Unforeseen

It is also noteworthy that Dumbledore does not stop Harry from receiving his Firebolt, even though he still believed Sirius a criminal at that point and it arrived in very suspicious circumstances.

'May I?' said Professor McGonagall, but she didn't wait for an answer before pulling the Firebolt out of their hands. She examined it carefully from handle to twig-ends. 'Hmm. And there was no note at all, Potter? No card? No message of any kind?'

'No,' said Harry blankly.

'I see ...' said Professor McGonagall. 'Well, I'm afraid I will have to take this, Potter.'

'W-what?' said Harry, scrambling to his feet. 'Why?'

'It will need to be checked for jinxes,' said Professor McGonagall.

[...]

'What did you go running to McGonagall for?'

Hermione threw her book aside. She was still pink in the face, but stood up and faced Ron defiantly.

'Because I thought - and Professor McGonagall agrees with me - that that broom was probably sent to Harry by Sirius Black!'

Harry Potter and the Prisoner of Azkaban - pp.171-2 - Bloomsbury - Chapter 11, The Firebolt

No I don't believe Dumbledore stole mail- not in the sense that Dobby did in Book 2 anyway.

After reading the whole series, we know that Dumbledore placed Harry with his aunt and uncle because of the protection that Lily offered. However, if we consider Dumbledore's conversation with Professor McGonagall at the start of the first film, he stated in response to her comments that he will be famous:

He's far better off growing up away from all of that. Until he is ready.

Dumbledore was a revered leader in the wizarding community such as decision would be respected and understood. Most likely, the majority would not have wanted to interfere in Dumbledore's known wish that Harry be given a normal childhood.

Evidence of this in the first book is where Harry recognises people in Diagon Alley including one gentleman that bowed his hat at him once. This demonstrates that witch and wizards were familiar with his appearance but were keeping a respectful distance.

For the minority, I imagine that the Dursley's home was, until Harry came of school age, registered as being muggle residence. So to protect the wizarding world from exposure, no mail was delivered. My supporting evidence of this would have been use of the Floo network in book/movie four. Arthur Weasley specific says that he had to have the Dursley's home added to the network specifically to collect Harry.