I like to use ECC even on the desktop, and yes there are ways to do it. At a cost.
On the Intel side, the CPU is not really the problem. "Small" Xeons like the E3-1225V3 are attractive for their price/performance even if you run them on desktop boards and don't use ECC support. In that setup they are like i7 parts with slightly lower clock speeds.
For the board though, the choices are limited and you have to shell out an additional 100 Euros or more for a "small server" board, because the typical desktop chipsets don't support ECC.
Add the extra price for the ECC RAM, maybe 50 Euros difference depending on how much RAM you want, and you end up paying something like 150 Euros extra.
AMD used to be really nice, with most processors (pre-Llano all desktop parts but Sempron) supporting ECC RAM and some mainboards also supporting it. The mainboard choices for ECC support were a bit limited, cheapskates like Asrock usually did not bother to support ECC RAM. So you might have had to pay 10 Euros more for the board, plus the above 50 Euros extra for the RAM. Made maybe 60 Euros difference to have ECC RAM in your rig.
Sadly, their APUs don't support ECC. AFAIK the FX line still does, but it is not really attractive compared to recent Intel models.