To Remove URL or not to Remove URL

I just removed several products that were discontinued from my ecommerce site. Now they are showing up in google webmaster tools as 404 (Not found). Should I request that google remove those particular urls or just let them slowly go away as google reindexes my site?

If they're appearing in your SERPs as 404s, I'd put through a removal request. It's always good to keep your listings free of 404s.

One more thought, have you updated your site map since the removals? If the old products are still listed on your Google site map, that's no doubt one reason why Google is finding these fresh 404s.

Yes I did remember to take them out of the Google site map.

How about making a custom 404 with a product index listing on it so if customers follow an old link from somewhere, they've got the option to move forward into the site?

Actually I do have a custom 404 for my customers that says "Sorry, the product was not found.
It was most likely discontinued.
Please use the site map or search box to find a similar item."

I'm just wondering what the best approach is as far as Google is concerned.

Do 301 redirection to the home page, some of them might be holding some PR that you can benefit of