The standard reaction to the death of anyone famous divides into two parts: the attempt to neatly fit them into the historical record, with authoritative claims about their significance and legacy; and personal reminiscence, with precious first-hand anecdotes trumping "what he/she meant to me" solipsism. The passing of Lou Reed has been an object case study.
Most media outlets have wheeled out Brian Eno's quote to the effect that everyone who bought the first Velvet's album formed a band. The quote dates from 1982, and was apparently based on Reed claiming that sales were only 30,000 in the first 5 years (1967-72). In fact, it is likely the record sold nearer 60,000 in the first couple of years after release, may have reached six figures in the early 70s, and has probably topped a million since then. My own personal recollection (I warned you) from the mid-70s is that the Velvet Underground and solo Lou Reed were as familiar to rock fans as Jethro Tull or The Byrds, and this owed relatively little to the personal recommendation of David Bowie.
I also recall buying the NME C81 mixtape in 1981. A running joke in the booklet that accompanied it was how every band had been influenced by the Velvets, which was perfectly credible when you consider the album included Cabaret Voltaire, DAF, Scritti Politti, the Buzzcocks and Orange Juice, among others. In other words, Eno was reflecting the widespread and longstanding influence of the Velvets (which had reached the point of parody) while insisting that this was still an interest limited to discerning avant-gardists like himself. What a knob.
The band catalyst trope has fought for top billing with tales of Reed's obnoxiousness in interviews, which are just opportunities for saddo journalists to try and filch some stardust. Some have seen this as the careful creation of a brand ("just showbusiness"), directly influenced by uber-commoditiser Andy Warhol, though the more thoughtful see determined authenticity. Others interpret it as the deliberate evasion of an "unknowable and contrary" man who valued privacy. The claim that it was an act has the ring of truth to it. You're not likely to have a lasting relationship with an artist and musician of the stature of Laurie Anderson if you're an irascible and selfish egotist in private too. Reed's confrontational stance and unwillingness to play the PR game owe much to his own romantic notions of the role of the artist (historical record bit coming up).
Reed's love of the marginal and despised has its roots in late nineteenth century decadence (which explains his interest in Frank Wedekind's Lulu). The template for his provocative public persona can be found in the original enfant terrible, the French poet and all-round reprobate Arthur Rimbaud, whose Une Saison en Enfer was translated by another poet, Delmore Schwartz, with whom Reed studied in the early 60s. A feature of the New York music scene, from the Beats and jazz experimentalists to Sonic Youth, has been the centrality of poetry and the role of the poet as critic/outsider. In this regard, French and American poetry have a lot more in common than either has with the British variety.
Poetry was a marginal taste in the UK music scene up to the late 70s (and tended towards the fey), where the Glam avant garde, exemplified by David Bowie and Roxy Music, was more influenced by visual art and theatre (hence the Ramones had a bigger impact here than Patti Smith, despite supportive media coverage for the "punk poet queen"). But the influence of Reed & co on provincial post-punk bands, like the Postcard stable and The Smiths, changed all that, reasserting the primacy of the heartfelt lyric after years of London irony and cut-up mannerisms. The major legacy of the Velvet Underground in the UK is landfill indie.
Bowie and Reed shared an interest in Berlin and the Weimar era, and both identified in their own ways with Isherwood's observer: "I am a camera with its shutter open, quite passive, recording, not thinking". But while Bowie (like Eno) was influenced by post-war German music, from Stockhausen to Krautrock, Reed remained more sonically conservative and essentially American (Perfect Day could have been sung by Doris Day), despite his best efforts on Metal Machine Music to prove otherwise. In the original Velvets mix, Reed provided the pop and John Cale the experimentation. For all his literary ambitions, Reed never deserted Tin Pan Alley.
The C81 joke worked because the modern bands, though different from each other, could be harnessed to a specific song or period in the Velvet Underground's back catalogue. This was a testament to the range and mutability (and even instability) of the original band: their naive enthusiasm for trying something different as much as their artistic pretensions. It was this range and unpredictability that Reed carried forward into his solo years, though his finest releases would be the "classic" pop songs of Transformer and the Velvet's out-take compilation, VU. In truth, he was just doodling from the mid-70s onwards.