For anybody spending more than a few days in Crete then it is well worth exploring the island. Crete is a BIG (160miles long), mountainous island so its advisable to hire a car if you wish to see the best of it - although buses / coaches and daily excursions do run from Rethymno centre to many of the places below.
Here are a few day trip options from Rethymno...
Day Trip Option 1
Balos Beach / Falassarna Beach
Balos Beach
This is a stunning beach but requires some effort to get to. It's a 2 hour drive, (one way), from Rethymno old town to Balos and the last 6 miles are down a dirt road. Finally on arriving at the Car Park you'll have a 20 minute walk down to Balos Bay. The dirt road itself is ok if you go slowly - we did it in a small hire car (and there were plenty of other small hire cars in the car park). A word of warning though - there is no phone signal and your hire car will most likely not be insured on the dirt road.
So why bother? Well it's one of the best beaches you can visit in Greece - it really is that good. Here are a few pics from our trip last year...
For more info see the Balos page.
Falassarna Beach / Spilios Taverna
If your heading to Balos then you will also pass close to Falassarna Beach. Another great beach and also well worth a visit. If you are hungry / thirsty then in Falassarna there is a good Taverna called Spilios.
Day Trip Option 2
Chania Town and Stefanou Beach
Chania Town
Chania is a great town/city and definitely worth a visit if you have time, (its about an hours drive from Rethymno). It is similar to Rethymno and arguably a bit nicer. There are lots of markets / cafes / galleries / restaurants / bars etc to explore and it also has a nice Old Town area for wandering around.
Stefanou Beach (or sometimes called Seitan Lamania Beach)
There is a nice beach on the way out/back from Chania called Stefanou Beach if you have time. Its a great beach that doesn't really come up in much of the Touristy information on Crete. Be warned though that the path down to the beach is difficult and there are parts that involve a little bit of clambering/climbing...
Day Trip Option 3
Preveli Beach
A cracking black/grey sand beach on the other side of the island to Rethymno (45 minute drive). There is a river / stream that flows into the beach that can be followed into a Palm lined gorge. If you want a very nice beach that is fairly close to Rethymno then this is your best option. You park at the top above the beach and then have a 15minute walk down - on the upside this gives you some fantastic views of the beach below...
Day Trip Option 4
Margarites Village
Fancy a relaxed day wandering a small Cretan village then Margarites is a good option. There are a few decent authentic Tavernas for food and drink but the biggest draw that Margarites has is all the Pottery shops. There are lots of them and even if pottery is not your thing (its not mine) they are still pretty interesting to wander around.
The other upside to Margarites is the drive in which affords you some great views over the Mountains and Valleys of Crete. The drive takes approx 35mins from Rethymno...
Day Trip Option 5
Samaria Gorge
Disclaimer... for the ambitious only (:

Samaria Gorge is a great day out but you will need to be up very early. Tours from Rethymno start at 5:30 - 6am! and really its a case of the earlier you can get to the start of the walk the better as the walk gets very crowded later in the day.
You are taken in a coach to the head of the gorge (about 2hrs drive). You then have a 16km trek all downhill passing through the gorge until you arrive on the beach in Aghia Roumeli (its then tradition to jump in the sea). The walk itself generally takes between 4-6 hours and is stunning.
When you arrive in Aghia Roumeli you can go to the beach or get a beer / food in one of the Tavernas. Later in the day a ferry will arrive to transport you along the coast to Chora Sfakion before then boarding the waiting coach to take you back to Rethymno.
For more info see the Samaria Gorge page.
Day Trip Option 6
Mili Gorge Walk
Our hotel and several guide books recommended this but unfortunately we ran out of time and never had chance to do it. Two nice villages here - Mili and Hromonastiri which you should visit and that are only a short 15-20 minute drive South of Rethymno. From just beneath the village of Mili there is a very good gorge walk that takes a couple of hours to complete.
The best way to do this is to take a taxi from Rethymno to the start of the path at Mili: it's not far (6km), and won't be expensive (the path is easy to find).
If driving then park where you see the sign “Gorge of Mills”. From the parking spot take a walk of roughly 300 metres to reach a traditional cafe - Mili Gorge Tavern - here you can get food / drink and info on the walk. Its a good Tavern with good views so should not be missed.
The path can be hard to follow in places so you should look for the red dots on trees and rocks. On completion of the walk you'll emerge at the coast a few km east of Rethymno, and can get a taxi or bus back to town from there - or walk. It's not a very long walk - a couple of hours, and very nice.
Here is a Map of the walk...
https://maps.google.com/maps/ms?msid=217442360984927778831.0004b1dbfd5c905dd9862&msa=0