The best excuse is the one which's truthful. The second best one is the one which's 'based on a true story' which, if properly administered, people won't look too closely into the details on, and if they do check, it generally checks out at first glance.
If yeu lie, eventually yeu'll get caught, and the purpose of making an excuse (to avoid awkward situations or harsh feelings) will just be doubled since now they both know AND they know yeu lied. Make too many lies, it turns into a messy web that makes no sense. It's better to just not lie in the first place if yeu can at all help it, and come up with something a bit more realistic.
If yeu were out drinking all night with coworkers, and are late for work, rather than saying yeur grandmother died, or yeu were in an accident or something, just make something vaguely true... "I spent the majority of the evening with intense social networking, it took a great deal of effort but I may have strengthened some ties within the company which could very well end up making things more effecient" is the kind of thing that managers love to hear. Unless they've used the same excuse themselves then they know yeu're bluffing. >.>; It helps if yeu stress things like "could very well" or "may have strengthened", they sound really good but are pretty much meaningless since they rely on the key term 'maybe', just masked behind better sounding phrazes which mean the same thing. Most people won't pick up on this though, especially if yeu actually stress them with just the right tone of voice to make it sound like yeu really believe it, even if yeu basically just said "pft I have no clue, doubtful but anything could happen". Yeu don't have to lie, so much as trick the person yeu're talking to into jumping to false conclusions. As long as everything yeu say is completely truthful, and the parts yeu state are accurate, they can even go back and check and yeu can confirm yeur story. Just make absolutely certain that, when they misinterpret yeu, if they ever come back to argue the matter that yeu enforce the guilt trip by stating that yeu were upfront and honest, and provided entirely accurate information (omit the part that yeu left key details and phrazing out) and that it's their own fault for misinterpreting the data yeu presented to them.
EDIT: Just realized I didn't provide an example for once >.>;;
Let's say a vase in the house is broken, yeur parents ask who broke it.
"Well I was out for most of the afternoon, so it would've been awfully hard for me to be at fault here. I don't know where my sister was, she might've been at home, I'm not sure, but it's possible she knows something about it."
This completely omits the fact that yeu were home for 15 minutes in the afternoon at the time that yeu knocked the vase over, and it kind of heavily implies that yeur sister did it (despite that yeu know full well that she didn't), but it's completely truthful as well. Yeu were gone most of the afternoon, if they check on that information they'll have proof of it. Yeu didn't know where yeur sister was (or brother or whotever), and it's possible she MAY know something about it (but probably not since she wasn't there at the time yeu broke it so this's probably safe). This turns the focus of the investigation away from yeurself and places the focus on a new prime suspect. All information was entirely truthful and accurate, there were just pieces omitted, and some parts which yeu had no evidence for, yeu stressed that because yeu didn't know, it seemed suspicious. Even though yeu know very well they weren't. In the end, yeu never directly denied breaking the vase, and yeu neatly skirted the issue. Acting surprised won't work either, too difficult to fake, it's easier to feign disinterest, especially if yeu're busy doing something else.
It doesn't matter if they're right. If they can't proove they're right, then they're wrong. No matter how right they may be.