I'm in the UK and I do both - receive PAYE from my employer (which sorts out my pension contribs, student loan repayments and national insurance/income tax payment), and I fill in an annual tax return to declare some additional income I receive. PAYE on its own is worked out on a simple code based on information you provide to your employer. I don't qualify for any breaks so mine is quite simple.
I quite enjoy filling in the tax return! My additional income is quite straightforward and I don't find the forms too difficult, it's more getting all the paperwork together. All I need to do is declare everything I've 'earned' (including bank account interest, although this is all taxed at source by the banks, so it's just to check which tax band I pay at). I file online and they write to me to let me know how much additional tax I owe, which they take from my salary through the PAYE system by adjusting my tax code (essentially they reduce my tax free sum, £10k, by the amount I owe).
If you earn over a certain amount (I can't remember how much) you have to do a tax return in the UK, but for the most part (and for most people) they take tax at source:
VAT - sales tax
Council tax - paid monthly to council via direct debit
Income tax - taken from salary at source
Savings account interest/dividend income - all received post tax.