And why not? So long as after the bubbly's been drunk you stop and put a more cautious hat on. Most of the time the offer will be entirely genuine and no need to read the small print, but that's no reason to trust them. This is a business arrangement and you need to stop feeling grateful that someone wants you - which is how we all feel, of course - and get real.
Take a friend of mine. A multi-published author, her agent presented her with some contracts to sign selling her e-book rights to her publisher. She did so without thinking - she assumed her agent would have checked that it was all OK. And it was, up to a point. Except, she sees her extensive backlist up on the publisher's website all at the same price as her paperbacks, with no additional marketing by the publisher and no advance up front and 25% of the non-existent royalties doesn't seem such a good deal. Especially as she's just been dropped by that publisher.
Take another author. First prize in short story competition - hooray! Publication in an anthology - whoopee! But copyright was handed over in the small print - which was a pity, given the anthology has been sold to the US with a vast print run (which the author wasn't notified of and only discovered accidently) so no royalties will be forthcoming. I've recently seen several short story comps which demand assignment of copyright as a condition of entry, which is outrageous - read the small print.
And then there are agents. I'm not talking about the obvious scammers - anyone can set themselves up as an agent so you have to be careful - but what about the legit agent who offers to represent your novel on the basis of, say, a win in a short story competition? I've heard of agents who seem to trawl the MAs and comps offering representation - a bit like talent spotters I suppose. There's no doubt that they're bona fide agents and get good deals for some of their clients, but an author should think before they commit themselves. Would they have chosen to approach this agent regardless? If yes, then fine. But if they would have been second or third (fourth, fifth etc) choice, why sign early, especially if you haven't yet started approaching other agents?
Finally, publishers. Publishing has changed dramatically over the last few years and continues to change so find out a bit about the publisher's background before you say yes. There are lots of small independent publishers around, but not all of them are as successful as others. Some are set up by well-meaning people who believe in good writing but have little idea of how to run a business. They may cope financially only because of grants (eg from the Arts Council), which might be removed. If a publisher goes bust, or only sells a few copies of your novel, then it will be unlikely you'll be able to get another deal for that book (though once you've got the rights back, you could always self/e-publish).
So, enjoy your moment of glory, but always read the small print and don't get carried away just because somebody wants you.