Vanguard are a mutually owned fund that specialise in index tracking investments. Because they are owned by the investors, they work to minimise the cost of running the funds (so don't pay out in commission, advertising etc). They are massive (about $4 Trillion in investor assets IIRC). As a result they are unlikely to go bust any time soon.
If you're looking to invest in index-trackers (S&P, FTSE, world, or one of their blended products, such as the LifeTrackers), they are about as safe an investment as you can get. If you're paranoid about the fund manager going bust, then you are covered up to £50,000 by the FSCS compensation scheme per institution so it may be prudent to spread investments amongst two or more investment brokers/funds if you've got more than this.
If you're not aware of it,
monevator.com is a good source of UK-based information.
Disclosure: I am not an IFA (so this advice is worth what you paid for it), and I have invested in Vanguard LifeStrategy.