This is really funny that you've brought this up, I thought I must be the only grown adult to have this issue!
We're currently on baby #3... and it has been varying degrees of awkward telling my parents with each pregnancy.
With our first, we literally got pregnant the second we were married (I was 27, we'd already been in a relationship for 4 years, were living together, and owned our own home) and made the announcement when we got back from our honeymoon, as DH's parents and my parents were together. We bought them all individual "grandma" and "grandpa" gifts (I got my mom the book, "Chicken soup for the grandmother's soul") and told them we wanted to thank them all for their help with the wedding... and when they opened the gifts everyone was really enthusiastic. BUT, I'm sure we only got that reaction because my MIL and FIL were there who immediately jumped up and started laughing and hugging everyone and totally took the awkwardness away. DH and I had to work ourselves up to making the announcement and I took 2 additional HPT's the day we told them JUST TO BE SURE. The following days were really awkward as my mom made all sorts of weird comments (like, "well you know, maybe you're not really pregnant...") and they just didn't know how to deal with it.
With our second baby, we had to tell my parents via Skype (we live in a different country than they do) and we had a "big brother in training" shirt for my DS, and when we told my parents they sort of paused and looked at each other and said, "well, I guess we'll have to cancel our vacation plans for next year so we can visit you instead..." and that was about it.
With our third baby, we did the same thing. Told my parents via Skype with a "Big sister" shirt for my DD and while they DID manage to congratulate us first, it just got really awkward and they changed the subject soon afterwards.
Like some other PP's though, I've never had an "open relationship" with either of my parents where we could talk about personal things and I think they just can't wrap their heads around the fact that DH and I (obviously) DTD and that equals babies.
The first announcement was the most nerve-wracking (I also had the feeling like I'd done something naughty!) but after that I just accepted that I was doing it more for me than I was for them, and DH and I like to laugh about how awkward my parents are now. Makes for a good story to tell friends ;-)
My advice though, would be the longer you put it off the more difficult it will be, and depending on how awkward your parents might be, the further along you are the more difficult it might be for them to process. My parents definitely needed the time to 'adjust' to the idea so we've always told them pretty early on to avoid any issues later. But that's just what has worked for us!